Pull back the curtain on infinity  
exploring the undesigned
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All positive-only PPPs under 1 million are available in CSV format.
There are 2221 of them under 1 million, and you can get them here.

 

    Revised July 2008.
    Data first published May 2007.
The High Primality of Prime-Derived Quadratic Sequences  
    Attention Math Students:
    This topic is not related to
    solving prime polynomials.
An analysis of the first 333 Proximate-Prime Polynomials for n = 0 to 1000  

 

    Now in Sloane's:
    OEIS Sequence A140947

 

 

 

  

 

 

 

 

    And the Winner Is...
    2n^2 - 2n + 53089

    634 primes in first 1000 terms
    OEIS Sequence A155557

The following results have been revised to show all PPPs with positive-only integers under 100,000.

Each quadratic sequence is obtained by looking at successive prime numbers and seeing if a 2nd degree polynomial relationship exists for four consecutive primes. The derived quadratic formula is then used to generate a long sequence, in this case 1000 terms, to see how many primes are generated. These proximate-prime polynomials are interesting because they exhibit much greater prime densities than other polynomials - 46 of them have greater than 50% prime values in this sample.

The results intriguingly show that all positive-integer PPPs have complex roots - only negative-integer PPPs have real roots. An interesting, but highly speculative, observation is that these PPPs overwhelmingly have a real part 1/2 or a multiple of 1/2. Anyone who has a nodding acquaintance with the Riemann Hypothesis may find this interesting. (RH's critical line is real = 1/2.) However, to balance that observation, it must be said that all polynomials with coefficients of 1 for x^2 and x have a real part 1/2 - even ones that don't produce any primes at all!

This Just In!
In each polynomial, the difference between the first and the fourth proximate primes appears to be a multiple of 6. While this simple-as-clockwork rule seems rather banal, this value could be related to the growth of the Riemann zeta function (specifically, the Lindelof hypothesis, a value that approaches 1/6th) and to the Basel problem (Euler's method for approximating Pi using infinite series, which works out to be (Pi^2)/6, as illustrated in ZetaTest).

(You can use QTest to generate complete sequences by entering the 4 proximate primes from a row in this table.)

Orange column shows the real part of the quadratic root.
Green column shows the density of primes in the first 1000 terms of the quadratic expression.


 
Proximate Primes Quadratic Finite Diff. Real Part Imag. Part Primes %
(n = 0 - 1000)
Sequence for n = 5 -> 15
(prime/composite)
17, 19, 23, 29   n^2 - n + 17  2 0.5 4.092676386  366  = 36.6   37, 47, 59, 73, 89, 107, 127, 149, 173, 199, 227 
41, 43, 47, 53   n^2 - n + 41  2 0.5 6.383572667  582  = 58.2   61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251 
79, 83, 89, 97   n^2 + n + 77  2 -0.5 8.760707734  246  = 24.6   107, 119, 133, 149, 167, 187, 209, 233, 259, 287, 317 
227, 229, 233, 239   n^2 - n + 227  2 0.5 15.05822035  445  = 44.5   247, 257, 269, 283, 299, 317, 337, 359, 383, 409, 437 
347, 349, 353, 359   n^2 - n + 347  2 0.5 18.62122445  412  = 41.2   367, 377, 389, 403, 419, 437, 457, 479, 503, 529, 557 
349, 353, 359, 367   n^2 + n + 347  2 -0.5 18.62122445  411  = 41.1   377, 389, 403, 419, 437, 457, 479, 503, 529, 557, 587 
379, 383, 389, 397   n^2 + n + 377  2 -0.5 19.41004894  418  = 41.8   407, 419, 433, 449, 467, 487, 509, 533, 559, 587, 617 
439, 443, 449, 457   n^2 + n + 437  2 -0.5 20.89856454  360  = 36.0   467, 479, 493, 509, 527, 547, 569, 593, 619, 647, 677 
569, 571, 577, 587   2n^2 - 4n + 571  4 1 16.86712779  347  = 34.7   601, 619, 641, 667, 697, 731, 769, 811, 857, 907, 961 
641, 643, 647, 653   n^2 - n + 641  2 0.5 25.31304012  368  = 36.8   661, 671, 683, 697, 713, 731, 751, 773, 797, 823, 851 
673, 677, 683, 691   n^2 + n + 671  2 -0.5 25.89884167  453  = 45.3   701, 713, 727, 743, 761, 781, 803, 827, 853, 881, 911 
677, 683, 691, 701   n^2 + 3n + 673  2 -1.5 25.89884167  453  = 45.3   713, 727, 743, 761, 781, 803, 827, 853, 881, 911, 943 
1031, 1033, 1039, 1049   2n^2 - 4n + 1033  4 1 22.70462508  471  = 47.1   1063, 1081, 1103, 1129, 1159, 1193, 1231, 1273, 1319, 1369, 1423 
1091, 1093, 1097, 1103   n^2 - n + 1091  2 0.5 33.02650451  314  = 31.4   1111, 1121, 1133, 1147, 1163, 1181, 1201, 1223, 1247, 1273, 1301 
1277, 1279, 1283, 1289   n^2 - n + 1277  2 0.5 35.73163864  456  = 45.6   1297, 1307, 1319, 1333, 1349, 1367, 1387, 1409, 1433, 1459, 1487 
1427, 1429, 1433, 1439   n^2 - n + 1427  2 0.5 37.77234438  426  = 42.6   1447, 1457, 1469, 1483, 1499, 1517, 1537, 1559, 1583, 1609, 1637 
1429, 1433, 1439, 1447   n^2 + n + 1427  2 -0.5 37.77234438  426  = 42.6   1457, 1469, 1483, 1499, 1517, 1537, 1559, 1583, 1609, 1637, 1667 
1487, 1489, 1493, 1499   n^2 - n + 1487  2 0.5 38.55839727  416  = 41.6   1507, 1517, 1529, 1543, 1559, 1577, 1597, 1619, 1643, 1669, 1697 
1549, 1553, 1559, 1567   n^2 + n + 1547  2 -0.5 39.32874267  265  = 26.5   1577, 1589, 1603, 1619, 1637, 1657, 1679, 1703, 1729, 1757, 1787 
1607, 1609, 1613, 1619   n^2 - n + 1607  2 0.5 40.0842862  386  = 38.6   1627, 1637, 1649, 1663, 1679, 1697, 1717, 1739, 1763, 1789, 1817 
1619, 1621, 1627, 1637   2n^2 - 4n + 1621  4 1 28.45171348  402  = 40.2   1651, 1669, 1691, 1717, 1747, 1781, 1819, 1861, 1907, 1957, 2011 
2203, 2207, 2213, 2221   n^2 + n + 2201  2 -0.5 46.91215194  457  = 45.7   2231, 2243, 2257, 2273, 2291, 2311, 2333, 2357, 2383, 2411, 2441 
2687, 2689, 2693, 2699   n^2 - n + 2687  2 0.5 51.83386924  355  = 35.5   2707, 2717, 2729, 2743, 2759, 2777, 2797, 2819, 2843, 2869, 2897 
2689, 2693, 2699, 2707   n^2 + n + 2687  2 -0.5 51.83386924  355  = 35.5   2717, 2729, 2743, 2759, 2777, 2797, 2819, 2843, 2869, 2897, 2927 
2711, 2713, 2719, 2729   2n^2 - 4n + 2713  4 1 36.81711559  326  = 32.6   2743, 2761, 2783, 2809, 2839, 2873, 2911, 2953, 2999, 3049, 3103 
2833, 2837, 2843, 2851   n^2 + n + 2831  2 -0.5 53.20479302  333  = 33.3   2861, 2873, 2887, 2903, 2921, 2941, 2963, 2987, 3013, 3041, 3071 
2903, 2909, 2917, 2927   n^2 + 3n + 2899  2 -1.5 53.82146412  352  = 35.2   2939, 2953, 2969, 2987, 3007, 3029, 3053, 3079, 3107, 3137, 3169 
2909, 2917, 2927, 2939   n^2 + 5n + 2903  2 -2.5 53.82146412  352  = 35.2   2953, 2969, 2987, 3007, 3029, 3053, 3079, 3107, 3137, 3169, 3203 
2917, 2927, 2939, 2953   n^2 + 7n + 2909  2 -3.5 53.82146412  351  = 35.1   2969, 2987, 3007, 3029, 3053, 3079, 3107, 3137, 3169, 3203, 3239 
3037, 3041, 3049, 3061   2n^2 - 2n + 3037  4 0.5 38.96472764  403  = 40.3   3077, 3097, 3121, 3149, 3181, 3217, 3257, 3301, 3349, 3401, 3457 
3527, 3529, 3533, 3539   n^2 - n + 3527  2 0.5 59.38644627  475  = 47.5   3547, 3557, 3569, 3583, 3599, 3617, 3637, 3659, 3683, 3709, 3737 
3539, 3541, 3547, 3557   2n^2 - 4n + 3541  4 1 42.06542523  409  = 40.9   3571, 3589, 3611, 3637, 3667, 3701, 3739, 3781, 3827, 3877, 3931 
3613, 3617, 3623, 3631   n^2 + n + 3611  2 -0.5 60.08951656  429  = 42.9   3641, 3653, 3667, 3683, 3701, 3721, 3743, 3767, 3793, 3821, 3851 
3917, 3919, 3923, 3929   n^2 - n + 3917  2 0.5 62.58394363  489  = 48.9   3937, 3947, 3959, 3973, 3989, 4007, 4027, 4049, 4073, 4099, 4127 
4001, 4003, 4007, 4013   n^2 - n + 4001  2 0.5 63.2514822  451  = 45.1   4021, 4031, 4043, 4057, 4073, 4091, 4111, 4133, 4157, 4183, 4211 
4127, 4129, 4133, 4139   n^2 - n + 4127  2 0.5 64.23978518  275  = 27.5   4147, 4157, 4169, 4183, 4199, 4217, 4237, 4259, 4283, 4309, 4337 
4637, 4639, 4643, 4649   n^2 - n + 4637  2 0.5 68.09368546  409  = 40.9   4657, 4667, 4679, 4693, 4709, 4727, 4747, 4769, 4793, 4819, 4847 
4787, 4789, 4793, 4799   n^2 - n + 4787  2 0.5 69.18634258  371  = 37.1   4807, 4817, 4829, 4843, 4859, 4877, 4897, 4919, 4943, 4969, 4997 
4931, 4933, 4937, 4943   n^2 - n + 4931  2 0.5 70.21929934  503  = 50.3   4951, 4961, 4973, 4987, 5003, 5021, 5041, 5063, 5087, 5113, 5141 
4933, 4937, 4943, 4951   n^2 + n + 4931  2 -0.5 70.21929934  503  = 50.3   4961, 4973, 4987, 5003, 5021, 5041, 5063, 5087, 5113, 5141, 5171 
6269, 6271, 6277, 6287   2n^2 - 4n + 6271  4 1 55.98660554  466  = 46.6   6301, 6319, 6341, 6367, 6397, 6431, 6469, 6511, 6557, 6607, 6661 
6701, 6703, 6709, 6719   2n^2 - 4n + 6703  4 1 57.88350369  420  = 42.0   6733, 6751, 6773, 6799, 6829, 6863, 6901, 6943, 6989, 7039, 7093 
6703, 6709, 6719, 6733   2n^2 + 6701  4 0 57.88350369  419  = 41.9   6751, 6773, 6799, 6829, 6863, 6901, 6943, 6989, 7039, 7093, 7151 
7211, 7213, 7219, 7229   2n^2 - 4n + 7213  4 1 60.04581584  490  = 49.0   7243, 7261, 7283, 7309, 7339, 7373, 7411, 7453, 7499, 7549, 7603 
8167, 8171, 8179, 8191   2n^2 - 2n + 8167  4 0.5 63.90031299  378  = 37.8   8207, 8227, 8251, 8279, 8311, 8347, 8387, 8431, 8479, 8531, 8587 
8231, 8233, 8237, 8243   n^2 - n + 8231  2 0.5 90.72348097  381  = 38.1   8251, 8261, 8273, 8287, 8303, 8321, 8341, 8363, 8387, 8413, 8441 
8363, 8369, 8377, 8387   n^2 + 3n + 8359  2 -1.5 91.41526131  464  = 46.4   8399, 8413, 8429, 8447, 8467, 8489, 8513, 8539, 8567, 8597, 8629 
8689, 8693, 8699, 8707   n^2 + n + 8687  2 -0.5 93.20273601  227  = 22.7   8717, 8729, 8743, 8759, 8777, 8797, 8819, 8843, 8869, 8897, 8927 
8933, 8941, 8951, 8963   n^2 + 5n + 8927  2 -2.5 94.44972207  406  = 40.6   8977, 8993, 9011, 9031, 9053, 9077, 9103, 9131, 9161, 9193, 9227 
9041, 9043, 9049, 9059   2n^2 - 4n + 9043  4 1 67.23466368  387  = 38.7   9073, 9091, 9113, 9139, 9169, 9203, 9241, 9283, 9329, 9379, 9433 
9281, 9283, 9293, 9311   4n^2 - 10n + 9287  8 1.25 48.16832465  450  = 45.0   9337, 9371, 9413, 9463, 9521, 9587, 9661, 9743, 9833, 9931, 10037 
9461, 9463, 9467, 9473   n^2 - n + 9461  2 0.5 97.26638679  412  = 41.2   9481, 9491, 9503, 9517, 9533, 9551, 9571, 9593, 9617, 9643, 9671 
10159, 10163, 10169, 10177   n^2 + n + 10157  2 -0.5 100.7807025  356  = 35.6   10187, 10199, 10213, 10229, 10247, 10267, 10289, 10313, 10339, 10367, 10397 
10331, 10333, 10337, 10343   n^2 - n + 10331  2 0.5 101.6402971  284  = 28.4   10351, 10361, 10373, 10387, 10403, 10421, 10441, 10463, 10487, 10513, 10541 
10627, 10631, 10639, 10651   2n^2 - 2n + 10627  4 0.5 72.89204346  493  = 49.3   10667, 10687, 10711, 10739, 10771, 10807, 10847, 10891, 10939, 10991, 11047 
11777, 11779, 11783, 11789   n^2 - n + 11777  2 0.5 108.5207353  525  = 52.5   11797, 11807, 11819, 11833, 11849, 11867, 11887, 11909, 11933, 11959, 11987 
12107, 12109, 12113, 12119   n^2 - n + 12107  2 0.5 110.0306775  519  = 51.9   12127, 12137, 12149, 12163, 12179, 12197, 12217, 12239, 12263, 12289, 12317 
12277, 12281, 12289, 12301   2n^2 - 2n + 12277  4 0.5 78.34698463  445  = 44.5   12317, 12337, 12361, 12389, 12421, 12457, 12497, 12541, 12589, 12641, 12697 
12409, 12413, 12421, 12433   2n^2 - 2n + 12409  4 0.5 78.76706164  401  = 40.1   12449, 12469, 12493, 12521, 12553, 12589, 12629, 12673, 12721, 12773, 12829 
12653, 12659, 12671, 12689   3n^2 - 3n + 12653  6 0.5 64.94164047  428  = 42.8   12713, 12743, 12779, 12821, 12869, 12923, 12983, 13049, 13121, 13199, 13283 
12791, 12799, 12809, 12821   n^2 + 5n + 12785  2 -2.5 113.0431334  348  = 34.8   12835, 12851, 12869, 12889, 12911, 12935, 12961, 12989, 13019, 13051, 13085 
12889, 12893, 12899, 12907   n^2 + n + 12887  2 -0.5 113.5198221  360  = 36.0   12917, 12929, 12943, 12959, 12977, 12997, 13019, 13043, 13069, 13097, 13127 
13463, 13469, 13477, 13487   n^2 + 3n + 13459  2 -1.5 116.0032327  462  = 46.2   13499, 13513, 13529, 13547, 13567, 13589, 13613, 13639, 13667, 13697, 13729 
13469, 13477, 13487, 13499   n^2 + 5n + 13463  2 -2.5 116.0032327  462  = 46.2   13513, 13529, 13547, 13567, 13589, 13613, 13639, 13667, 13697, 13729, 13763 
13477, 13487, 13499, 13513   n^2 + 7n + 13469  2 -3.5 116.0032327  461  = 46.1   13529, 13547, 13567, 13589, 13613, 13639, 13667, 13697, 13729, 13763, 13799 
13829, 13831, 13841, 13859   4n^2 - 10n + 13835  8 1.25 58.79785285  283  = 28.3   13885, 13919, 13961, 14011, 14069, 14135, 14209, 14291, 14381, 14479, 14585 
13901, 13903, 13907, 13913   n^2 - n + 13901  2 0.5 117.9014419  494  = 49.4   13921, 13931, 13943, 13957, 13973, 13991, 14011, 14033, 14057, 14083, 14111 
13903, 13907, 13913, 13921   n^2 + n + 13901  2 -0.5 117.9014419  493  = 49.3   13931, 13943, 13957, 13973, 13991, 14011, 14033, 14057, 14083, 14111, 14141 
13907, 13913, 13921, 13931   n^2 + 3n + 13903  2 -1.5 117.9014419  492  = 49.2   13943, 13957, 13973, 13991, 14011, 14033, 14057, 14083, 14111, 14141, 14173 
14083, 14087, 14107, 14143   8n^2 - 20n + 14095  16 1.25 41.95607822  332  = 33.2   14195, 14263, 14347, 14447, 14563, 14695, 14843, 15007, 15187, 15383, 15595 
14627, 14629, 14633, 14639   n^2 - n + 14627  2 0.5 120.9411014  528  = 52.8   14647, 14657, 14669, 14683, 14699, 14717, 14737, 14759, 14783, 14809, 14837 
14657, 14669, 14683, 14699   n^2 + 9n + 14647  2 -4.5 120.9411014  525  = 52.5   14717, 14737, 14759, 14783, 14809, 14837, 14867, 14899, 14933, 14969, 15007 
14713, 14717, 14723, 14731   n^2 + n + 14711  2 -0.5 121.2878807  528  = 52.8   14741, 14753, 14767, 14783, 14801, 14821, 14843, 14867, 14893, 14921, 14951 
15073, 15077, 15083, 15091   n^2 + n + 15071  2 -0.5 122.762983  331  = 33.1   15101, 15113, 15127, 15143, 15161, 15181, 15203, 15227, 15253, 15281, 15311 
15077, 15083, 15091, 15101   n^2 + 3n + 15073  2 -1.5 122.762983  331  = 33.1   15113, 15127, 15143, 15161, 15181, 15203, 15227, 15253, 15281, 15311, 15343 
15269, 15271, 15277, 15287   2n^2 - 4n + 15271  4 1 87.37562589  315  = 31.5   15301, 15319, 15341, 15367, 15397, 15431, 15469, 15511, 15557, 15607, 15661 
15373, 15377, 15383, 15391   n^2 + n + 15371  2 -0.5 123.9788288  513  = 51.3   15401, 15413, 15427, 15443, 15461, 15481, 15503, 15527, 15553, 15581, 15611 
15377, 15383, 15391, 15401   n^2 + 3n + 15373  2 -1.5 123.9788288  514  = 51.4   15413, 15427, 15443, 15461, 15481, 15503, 15527, 15553, 15581, 15611, 15643 
15383, 15391, 15401, 15413   n^2 + 5n + 15377  2 -2.5 123.9788288  513  = 51.3   15427, 15443, 15461, 15481, 15503, 15527, 15553, 15581, 15611, 15643, 15677 
15391, 15401, 15413, 15427   n^2 + 7n + 15383  2 -3.5 123.9788288  512  = 51.2   15443, 15461, 15481, 15503, 15527, 15553, 15581, 15611, 15643, 15677, 15713 
15551, 15559, 15569, 15581   n^2 + 5n + 15545  2 -2.5 124.6545226  421  = 42.1   15595, 15611, 15629, 15649, 15671, 15695, 15721, 15749, 15779, 15811, 15845 
17093, 17099, 17107, 17117   n^2 + 3n + 17089  2 -1.5 130.7162958  317  = 31.7   17129, 17143, 17159, 17177, 17197, 17219, 17243, 17269, 17297, 17327, 17359 
17117, 17123, 17137, 17159   4n^2 - 6n + 17119  8 0.75 65.41549893  277  = 27.7   17189, 17227, 17273, 17327, 17389, 17459, 17537, 17623, 17717, 17819, 17929 
17327, 17333, 17341, 17351   n^2 + 3n + 17323  2 -1.5 131.6083204  395  = 39.5   17363, 17377, 17393, 17411, 17431, 17453, 17477, 17503, 17531, 17561, 17593 
17747, 17749, 17761, 17783   5n^2 - 13n + 17755  10 1.3 59.57608581  257  = 25.7   17815, 17857, 17909, 17971, 18043, 18125, 18217, 18319, 18431, 18553, 18685 
17921, 17923, 17929, 17939   2n^2 - 4n + 17923  4 1 94.6599176  367  = 36.7   17953, 17971, 17993, 18019, 18049, 18083, 18121, 18163, 18209, 18259, 18313 
19709, 19717, 19727, 19739   n^2 + 5n + 19703  2 -2.5 140.3451104  442  = 44.2   19753, 19769, 19787, 19807, 19829, 19853, 19879, 19907, 19937, 19969, 20003 
19913, 19919, 19927, 19937   n^2 + 3n + 19909  2 -1.5 141.0912825  451  = 45.1   19949, 19963, 19979, 19997, 20017, 20039, 20063, 20089, 20117, 20147, 20179 
19919, 19927, 19937, 19949   n^2 + 5n + 19913  2 -2.5 141.0912825  451  = 45.1   19963, 19979, 19997, 20017, 20039, 20063, 20089, 20117, 20147, 20179, 20213 
20323, 20327, 20333, 20341   n^2 + n + 20321  2 -0.5 142.5508681  372  = 37.2   20351, 20363, 20377, 20393, 20411, 20431, 20453, 20477, 20503, 20531, 20561 
20389, 20393, 20399, 20407   n^2 + n + 20387  2 -0.5 142.7821768  392  = 39.2   20417, 20429, 20443, 20459, 20477, 20497, 20519, 20543, 20569, 20597, 20627 
20747, 20749, 20753, 20759   n^2 - n + 20747  2 0.5 144.0373216  486  = 48.6   20767, 20777, 20789, 20803, 20819, 20837, 20857, 20879, 20903, 20929, 20957 
20873, 20879, 20887, 20897   n^2 + 3n + 20869  2 -1.5 144.4532796  229  = 22.9   20909, 20923, 20939, 20957, 20977, 20999, 21023, 21049, 21077, 21107, 21139 
21139, 21143, 21149, 21157   n^2 + n + 21137  2 -0.5 145.3848341  521  = 52.1   21167, 21179, 21193, 21209, 21227, 21247, 21269, 21293, 21319, 21347, 21377 
21557, 21559, 21563, 21569   n^2 - n + 21557  2 0.5 146.8221714  534  = 53.4   21577, 21587, 21599, 21613, 21629, 21647, 21667, 21689, 21713, 21739, 21767 
21559, 21563, 21569, 21577   n^2 + n + 21557  2 -0.5 146.8221714  534  = 53.4   21587, 21599, 21613, 21629, 21647, 21667, 21689, 21713, 21739, 21767, 21797 
21563, 21569, 21577, 21587   n^2 + 3n + 21559  2 -1.5 146.8221714  533  = 53.3   21599, 21613, 21629, 21647, 21667, 21689, 21713, 21739, 21767, 21797, 21829 
21863, 21871, 21881, 21893   n^2 + 5n + 21857  2 -2.5 147.8199919  293  = 29.3   21907, 21923, 21941, 21961, 21983, 22007, 22033, 22061, 22091, 22123, 22157 
21997, 22003, 22013, 22027   2n^2 + 21995  4 0 104.8689659  385  = 38.5   22045, 22067, 22093, 22123, 22157, 22195, 22237, 22283, 22333, 22387, 22445 
22279, 22283, 22291, 22303   2n^2 - 2n + 22279  4 0.5 105.5426454  320  = 32.0   22319, 22339, 22363, 22391, 22423, 22459, 22499, 22543, 22591, 22643, 22699 
22739, 22741, 22751, 22769   4n^2 - 10n + 22745  8 1.25 75.39686665  299  = 29.9   22795, 22829, 22871, 22921, 22979, 23045, 23119, 23201, 23291, 23389, 23495 
23081, 23087, 23099, 23117   3n^2 - 3n + 23081  6 0.5 87.71212383  359  = 35.9   23141, 23171, 23207, 23249, 23297, 23351, 23411, 23477, 23549, 23627, 23711 
23669, 23671, 23677, 23687   2n^2 - 4n + 23671  4 1 108.7864881  586  = 58.6   23701, 23719, 23741, 23767, 23797, 23831, 23869, 23911, 23957, 24007, 24061 
23741, 23743, 23747, 23753   n^2 - n + 23741  2 0.5 154.0803362  401  = 40.1   23761, 23771, 23783, 23797, 23813, 23831, 23851, 23873, 23897, 23923, 23951 
23743, 23747, 23753, 23761   n^2 + n + 23741  2 -0.5 154.0803362  400  = 40.0   23771, 23783, 23797, 23813, 23831, 23851, 23873, 23897, 23923, 23951, 23981 
23869, 23873, 23879, 23887   n^2 + n + 23867  2 -0.5 154.4886727  459  = 45.9   23897, 23909, 23923, 23939, 23957, 23977, 23999, 24023, 24049, 24077, 24107 
24109, 24113, 24121, 24133   2n^2 - 2n + 24109  4 0.5 109.7918485  411  = 41.1   24149, 24169, 24193, 24221, 24253, 24289, 24329, 24373, 24421, 24473, 24529 
25243, 25247, 25253, 25261   n^2 + n + 25241  2 -0.5 158.8733773  459  = 45.9   25271, 25283, 25297, 25313, 25331, 25351, 25373, 25397, 25423, 25451, 25481 
25339, 25343, 25349, 25357   n^2 + n + 25337  2 -0.5 159.1752179  382  = 38.2   25367, 25379, 25393, 25409, 25427, 25447, 25469, 25493, 25519, 25547, 25577 
25343, 25349, 25357, 25367   n^2 + 3n + 25339  2 -1.5 159.1752179  382  = 38.2   25379, 25393, 25409, 25427, 25447, 25469, 25493, 25519, 25547, 25577, 25609 
25577, 25579, 25583, 25589   n^2 - n + 25577  2 0.5 159.9273272  335  = 33.5   25597, 25607, 25619, 25633, 25649, 25667, 25687, 25709, 25733, 25759, 25787 
26017, 26021, 26029, 26041   2n^2 - 2n + 26017  4 0.5 114.0537154  335  = 33.5   26057, 26077, 26101, 26129, 26161, 26197, 26237, 26281, 26329, 26381, 26437 
26393, 26399, 26407, 26417   n^2 + 3n + 26389  2 -1.5 162.4399889  331  = 33.1   26429, 26443, 26459, 26477, 26497, 26519, 26543, 26569, 26597, 26627, 26659 
26681, 26683, 26687, 26693   n^2 - n + 26681  2 0.5 163.3424317  504  = 50.4   26701, 26711, 26723, 26737, 26753, 26771, 26791, 26813, 26837, 26863, 26891 
26711, 26713, 26717, 26723   n^2 - n + 26711  2 0.5 163.4342375  370  = 37.0   26731, 26741, 26753, 26767, 26783, 26801, 26821, 26843, 26867, 26893, 26921 
26891, 26893, 26903, 26921   4n^2 - 10n + 26897  8 1.25 81.99199656  313  = 31.3   26947, 26981, 27023, 27073, 27131, 27197, 27271, 27353, 27443, 27541, 27647 
27281, 27283, 27299, 27329   7n^2 - 19n + 27293  14 1.357142857 62.42722293  329  = 32.9   27373, 27431, 27503, 27589, 27689, 27803, 27931, 28073, 28229, 28399, 28583 
27737, 27739, 27743, 27749   n^2 - n + 27737  2 0.5 166.5435379  488  = 48.8   27757, 27767, 27779, 27793, 27809, 27827, 27847, 27869, 27893, 27919, 27947 
27799, 27803, 27809, 27817   n^2 + n + 27797  2 -0.5 166.7235736  210  = 21.0   27827, 27839, 27853, 27869, 27887, 27907, 27929, 27953, 27979, 28007, 28037 
27941, 27943, 27947, 27953   n^2 - n + 27941  2 0.5 167.1548683  599  = 59.9   27961, 27971, 27983, 27997, 28013, 28031, 28051, 28073, 28097, 28123, 28151 
27943, 27947, 27953, 27961   n^2 + n + 27941  2 -0.5 167.1548683  599  = 59.9   27971, 27983, 27997, 28013, 28031, 28051, 28073, 28097, 28123, 28151, 28181 
28277, 28279, 28283, 28289   n^2 - n + 28277  2 0.5 168.1569208  518  = 51.8   28297, 28307, 28319, 28333, 28349, 28367, 28387, 28409, 28433, 28459, 28487 
28279, 28283, 28289, 28297   n^2 + n + 28277  2 -0.5 168.1569208  518  = 51.8   28307, 28319, 28333, 28349, 28367, 28387, 28409, 28433, 28459, 28487, 28517 
28283, 28289, 28297, 28307   n^2 + 3n + 28279  2 -1.5 168.1569208  518  = 51.8   28319, 28333, 28349, 28367, 28387, 28409, 28433, 28459, 28487, 28517, 28549 
28429, 28433, 28439, 28447   n^2 + n + 28427  2 -0.5 168.6023428  306  = 30.6   28457, 28469, 28483, 28499, 28517, 28537, 28559, 28583, 28609, 28637, 28667 
28753, 28759, 28771, 28789   3n^2 - 3n + 28753  6 0.5 97.89833162  560  = 56.0   28813, 28843, 28879, 28921, 28969, 29023, 29083, 29149, 29221, 29299, 29383 
29021, 29023, 29027, 29033   n^2 - n + 29021  2 0.5 170.3547769  400  = 40.0   29041, 29051, 29063, 29077, 29093, 29111, 29131, 29153, 29177, 29203, 29231 
29059, 29063, 29077, 29101   5n^2 - 11n + 29065  10 1.1 76.2350969  262  = 26.2   29135, 29179, 29233, 29297, 29371, 29455, 29549, 29653, 29767, 29891, 30025 
29129, 29131, 29137, 29147   2n^2 - 4n + 29131  4 1 120.6834703  348  = 34.8   29161, 29179, 29201, 29227, 29257, 29291, 29329, 29371, 29417, 29467, 29521 
29473, 29483, 29501, 29527   4n^2 - 2n + 29471  8 0.25 85.83523461  228  = 22.8   29561, 29603, 29653, 29711, 29777, 29851, 29933, 30023, 30121, 30227, 30341 
30851, 30853, 30859, 30869   2n^2 - 4n + 30853  4 1 124.1994364  406  = 40.6   30883, 30901, 30923, 30949, 30979, 31013, 31051, 31093, 31139, 31189, 31243 
31247, 31249, 31253, 31259   n^2 - n + 31247  2 0.5 176.7675027  487  = 48.7   31267, 31277, 31289, 31303, 31319, 31337, 31357, 31379, 31403, 31429, 31457 
31249, 31253, 31259, 31267   n^2 + n + 31247  2 -0.5 176.7675027  487  = 48.7   31277, 31289, 31303, 31319, 31337, 31357, 31379, 31403, 31429, 31457, 31487 
31793, 31799, 31817, 31847   6n^2 - 12n + 31799  12 1 72.79308575  249  = 24.9   31889, 31943, 32009, 32087, 32177, 32279, 32393, 32519, 32657, 32807, 32969 
31973, 31981, 31991, 32003   n^2 + 5n + 31967  2 -2.5 178.7756975  428  = 42.8   32017, 32033, 32051, 32071, 32093, 32117, 32143, 32171, 32201, 32233, 32267 
32057, 32059, 32063, 32069   n^2 - n + 32057  2 0.5 179.043989  395  = 39.5   32077, 32087, 32099, 32113, 32129, 32147, 32167, 32189, 32213, 32239, 32267 
32059, 32063, 32069, 32077   n^2 + n + 32057  2 -0.5 179.043989  395  = 39.5   32087, 32099, 32113, 32129, 32147, 32167, 32189, 32213, 32239, 32267, 32297 
32297, 32299, 32303, 32309   n^2 - n + 32297  2 0.5 179.7129656  460  = 46.0   32317, 32327, 32339, 32353, 32369, 32387, 32407, 32429, 32453, 32479, 32507 
32569, 32573, 32579, 32587   n^2 + n + 32567  2 -0.5 180.4626  369  = 36.9   32597, 32609, 32623, 32639, 32657, 32677, 32699, 32723, 32749, 32777, 32807 
32611, 32621, 32633, 32647   n^2 + 7n + 32603  2 -3.5 180.5290835  367  = 36.7   32663, 32681, 32701, 32723, 32747, 32773, 32801, 32831, 32863, 32897, 32933 
32779, 32783, 32789, 32797   n^2 + n + 32777  2 -0.5 181.0435031  512  = 51.2   32807, 32819, 32833, 32849, 32867, 32887, 32909, 32933, 32959, 32987, 33017 
33149, 33151, 33161, 33179   4n^2 - 10n + 33155  8 1.25 91.0339909  310  = 31.0   33205, 33239, 33281, 33331, 33389, 33455, 33529, 33611, 33701, 33799, 33905 
33199, 33203, 33211, 33223   2n^2 - 2n + 33199  4 0.5 128.8380767  439  = 43.9   33239, 33259, 33283, 33311, 33343, 33379, 33419, 33463, 33511, 33563, 33619 
33347, 33349, 33353, 33359   n^2 - n + 33347  2 0.5 182.6109252  502  = 50.2   33367, 33377, 33389, 33403, 33419, 33437, 33457, 33479, 33503, 33529, 33557 
33617, 33619, 33623, 33629   n^2 - n + 33617  2 0.5 183.3487115  528  = 52.8   33637, 33647, 33659, 33673, 33689, 33707, 33727, 33749, 33773, 33799, 33827 
33619, 33623, 33629, 33637   n^2 + n + 33617  2 -0.5 183.3487115  528  = 52.8   33647, 33659, 33673, 33689, 33707, 33727, 33749, 33773, 33799, 33827, 33857 
33749, 33751, 33757, 33767   2n^2 - 4n + 33751  4 1 129.9018861  349  = 34.9   33781, 33799, 33821, 33847, 33877, 33911, 33949, 33991, 34037, 34087, 34141 
34267, 34273, 34283, 34297   2n^2 + 34265  4 0 130.8911762  301  = 30.1   34315, 34337, 34363, 34393, 34427, 34465, 34507, 34553, 34603, 34657, 34715 
34313, 34319, 34327, 34337   n^2 + 3n + 34309  2 -1.5 185.2208142  221  = 22.1   34349, 34363, 34379, 34397, 34417, 34439, 34463, 34489, 34517, 34547, 34579 
34367, 34369, 34381, 34403   5n^2 - 13n + 34375  10 1.3 82.90542805  241  = 24.1   34435, 34477, 34529, 34591, 34663, 34745, 34837, 34939, 35051, 35173, 35305 
35051, 35053, 35059, 35069   2n^2 - 4n + 35053  4 1 132.3839114  295  = 29.5   35083, 35101, 35123, 35149, 35179, 35213, 35251, 35293, 35339, 35389, 35443 
35081, 35083, 35089, 35099   2n^2 - 4n + 35083  4 1 132.4405527  322  = 32.2   35113, 35131, 35153, 35179, 35209, 35243, 35281, 35323, 35369, 35419, 35473 
35531, 35533, 35537, 35543   n^2 - n + 35531  2 0.5 188.4960212  488  = 48.8   35551, 35561, 35573, 35587, 35603, 35621, 35641, 35663, 35687, 35713, 35741 
35591, 35593, 35597, 35603   n^2 - n + 35591  2 0.5 188.6551086  434  = 43.4   35611, 35621, 35633, 35647, 35663, 35681, 35701, 35723, 35747, 35773, 35801 
36067, 36073, 36083, 36097   2n^2 + 36065  4 0 134.2851444  337  = 33.7   36115, 36137, 36163, 36193, 36227, 36265, 36307, 36353, 36403, 36457, 36515 
36467, 36469, 36473, 36479   n^2 - n + 36467  2 0.5 190.9626927  403  = 40.3   36487, 36497, 36509, 36523, 36539, 36557, 36577, 36599, 36623, 36649, 36677 
36559, 36563, 36571, 36583   2n^2 - 2n + 36559  4 0.5 135.2007766  519  = 51.9   36599, 36619, 36643, 36671, 36703, 36739, 36779, 36823, 36871, 36923, 36979 
37361, 37363, 37369, 37379   2n^2 - 4n + 37363  4 1 136.6766257  363  = 36.3   37393, 37411, 37433, 37459, 37489, 37523, 37561, 37603, 37649, 37699, 37753 
37571, 37573, 37579, 37589   2n^2 - 4n + 37573  4 1 137.0602057  510  = 51.0   37603, 37621, 37643, 37669, 37699, 37733, 37771, 37813, 37859, 37909, 37963 
37693, 37699, 37717, 37747   6n^2 - 12n + 37699  12 1 79.26012028  321  = 32.1   37789, 37843, 37909, 37987, 38077, 38179, 38293, 38419, 38557, 38707, 38869 
37847, 37853, 37861, 37871   n^2 + 3n + 37843  2 -1.5 194.5269904  368  = 36.8   37883, 37897, 37913, 37931, 37951, 37973, 37997, 38023, 38051, 38081, 38113 
38447, 38449, 38453, 38459   n^2 - n + 38447  2 0.5 196.0784282  316  = 31.6   38467, 38477, 38489, 38503, 38519, 38537, 38557, 38579, 38603, 38629, 38657 
38723, 38729, 38737, 38747   n^2 + 3n + 38719  2 -1.5 196.7657236  349  = 34.9   38759, 38773, 38789, 38807, 38827, 38849, 38873, 38899, 38927, 38957, 38989 
38971, 38977, 38993, 39019   5n^2 - 9n + 38975  10 0.9 88.28470989  315  = 31.5   39055, 39101, 39157, 39223, 39299, 39385, 39481, 39587, 39703, 39829, 39965 
39227, 39229, 39233, 39239   n^2 - n + 39227  2 0.5 198.0574412  461  = 46.1   39247, 39257, 39269, 39283, 39299, 39317, 39337, 39359, 39383, 39409, 39437 
39761, 39769, 39779, 39791   n^2 + 5n + 39755  2 -2.5 199.3708855  338  = 33.8   39805, 39821, 39839, 39859, 39881, 39905, 39931, 39959, 39989, 40021, 40055 
39839, 39841, 39847, 39857   2n^2 - 4n + 39841  4 1 141.1364588  382  = 38.2   39871, 39889, 39911, 39937, 39967, 40001, 40039, 40081, 40127, 40177, 40231 
40591, 40597, 40609, 40627   3n^2 - 3n + 40591  6 0.5 116.3188864  290  = 29.0   40651, 40681, 40717, 40759, 40807, 40861, 40921, 40987, 41059, 41137, 41221 
41177, 41179, 41183, 41189   n^2 - n + 41177  2 0.5 202.920551  376  = 37.6   41197, 41207, 41219, 41233, 41249, 41267, 41287, 41309, 41333, 41359, 41387 
41263, 41269, 41281, 41299   3n^2 - 3n + 41263  6 0.5 117.2778041  373  = 37.3   41323, 41353, 41389, 41431, 41479, 41533, 41593, 41659, 41731, 41809, 41893 
41651, 41659, 41669, 41681   n^2 + 5n + 41645  2 -2.5 204.0557522  373  = 37.3   41695, 41711, 41729, 41749, 41771, 41795, 41821, 41849, 41879, 41911, 41945 
41893, 41897, 41903, 41911   n^2 + n + 41891  2 -0.5 204.6722991  423  = 42.3   41921, 41933, 41947, 41963, 41981, 42001, 42023, 42047, 42073, 42101, 42131 
42227, 42239, 42257, 42281   3n^2 + 3n + 42221  6 -0.5 118.631432  351  = 35.1   42311, 42347, 42389, 42437, 42491, 42551, 42617, 42689, 42767, 42851, 42941 
42433, 42437, 42443, 42451   n^2 + n + 42431  2 -0.5 205.9872569  403  = 40.3   42461, 42473, 42487, 42503, 42521, 42541, 42563, 42587, 42613, 42641, 42671 
42461, 42463, 42467, 42473   n^2 - n + 42461  2 0.5 206.0600641  396  = 39.6   42481, 42491, 42503, 42517, 42533, 42551, 42571, 42593, 42617, 42643, 42671 
42701, 42703, 42709, 42719   2n^2 - 4n + 42703  4 1 146.1181029  593  = 59.3   42733, 42751, 42773, 42799, 42829, 42863, 42901, 42943, 42989, 43039, 43093 
43103, 43117, 43133, 43151   n^2 + 11n + 43091  2 -5.5 207.5108431  379  = 37.9   43171, 43193, 43217, 43243, 43271, 43301, 43333, 43367, 43403, 43441, 43481 
43481, 43487, 43499, 43517   3n^2 - 3n + 43481  6 0.5 120.3886069  394  = 39.4   43541, 43571, 43607, 43649, 43697, 43751, 43811, 43877, 43949, 44027, 44111 
43487, 43499, 43517, 43541   3n^2 + 3n + 43481  6 -0.5 120.3886069  394  = 39.4   43571, 43607, 43649, 43697, 43751, 43811, 43877, 43949, 44027, 44111, 44201 
44171, 44179, 44189, 44201   n^2 + 5n + 44165  2 -2.5 210.1398344  290  = 29.0   44215, 44231, 44249, 44269, 44291, 44315, 44341, 44369, 44399, 44431, 44465 
44267, 44269, 44273, 44279   n^2 - n + 44267  2 0.5 210.3966492  436  = 43.6   44287, 44297, 44309, 44323, 44339, 44357, 44377, 44399, 44423, 44449, 44477 
44531, 44533, 44537, 44543   n^2 - n + 44531  2 0.5 211.023103  359  = 35.9   44551, 44561, 44573, 44587, 44603, 44621, 44641, 44663, 44687, 44713, 44741 
44699, 44701, 44711, 44729   4n^2 - 10n + 44705  8 1.25 105.7103945  388  = 38.8   44755, 44789, 44831, 44881, 44939, 45005, 45079, 45161, 45251, 45349, 45455 
44909, 44917, 44927, 44939   n^2 + 5n + 44903  2 -2.5 211.888532  391  = 39.1   44953, 44969, 44987, 45007, 45029, 45053, 45079, 45107, 45137, 45169, 45203 
44917, 44927, 44939, 44953   n^2 + 7n + 44909  2 -3.5 211.888532  391  = 39.1   44969, 44987, 45007, 45029, 45053, 45079, 45107, 45137, 45169, 45203, 45239 
44959, 44963, 44971, 44983   2n^2 - 2n + 44959  4 0.5 149.9308174  318  = 31.8   44999, 45019, 45043, 45071, 45103, 45139, 45179, 45223, 45271, 45323, 45379 
45589, 45599, 45613, 45631   2n^2 + 4n + 45583  4 -1 150.9652278  436  = 43.6   45653, 45679, 45709, 45743, 45781, 45823, 45869, 45919, 45973, 46031, 46093 
45821, 45823, 45827, 45833   n^2 - n + 45821  2 0.5 214.0578193  414  = 41.4   45841, 45851, 45863, 45877, 45893, 45911, 45931, 45953, 45977, 46003, 46031 
45823, 45827, 45833, 45841   n^2 + n + 45821  2 -0.5 214.0578193  413  = 41.3   45851, 45863, 45877, 45893, 45911, 45931, 45953, 45977, 46003, 46031, 46061 
46183, 46187, 46199, 46219   4n^2 - 8n + 46187  8 1 107.4511517  376  = 37.6   46247, 46283, 46327, 46379, 46439, 46507, 46583, 46667, 46759, 46859, 46967 
46589, 46591, 46601, 46619   4n^2 - 10n + 46595  8 1.25 107.9221363  257  = 25.7   46645, 46679, 46721, 46771, 46829, 46895, 46969, 47051, 47141, 47239, 47345 
46687, 46691, 46703, 46723   4n^2 - 8n + 46691  8 1 108.0358737  388  = 38.8   46751, 46787, 46831, 46883, 46943, 47011, 47087, 47171, 47263, 47363, 47471 
47119, 47123, 47129, 47137   n^2 + n + 47117  2 -0.5 217.0639307  322  = 32.2   47147, 47159, 47173, 47189, 47207, 47227, 47249, 47273, 47299, 47327, 47357 
47351, 47353, 47363, 47381   4n^2 - 10n + 47357  8 1.25 108.8011374  392  = 39.2   47407, 47441, 47483, 47533, 47591, 47657, 47731, 47813, 47903, 48001, 48107 
47623, 47629, 47639, 47653   2n^2 + 47621  4 0 154.3065131  226  = 22.6   47671, 47693, 47719, 47749, 47783, 47821, 47863, 47909, 47959, 48013, 48071 
47807, 47809, 47819, 47837   4n^2 - 10n + 47813  8 1.25 109.3237737  358  = 35.8   47863, 47897, 47939, 47989, 48047, 48113, 48187, 48269, 48359, 48457, 48563 
48073, 48079, 48091, 48109   3n^2 - 3n + 48073  6 0.5 126.5862683  412  = 41.2   48133, 48163, 48199, 48241, 48289, 48343, 48403, 48469, 48541, 48619, 48703 
49031, 49033, 49037, 49043   n^2 - n + 49031  2 0.5 221.4288825  504  = 50.4   49051, 49061, 49073, 49087, 49103, 49121, 49141, 49163, 49187, 49213, 49241 
49529, 49531, 49537, 49547   2n^2 - 4n + 49531  4 1 157.3674045  281  = 28.1   49561, 49579, 49601, 49627, 49657, 49691, 49729, 49771, 49817, 49867, 49921 
49597, 49603, 49613, 49627   2n^2 + 49595  4 0 157.4722198  226  = 22.6   49645, 49667, 49693, 49723, 49757, 49795, 49837, 49883, 49933, 49987, 50045 
49739, 49741, 49747, 49757   2n^2 - 4n + 49741  4 1 157.7006658  430  = 43.0   49771, 49789, 49811, 49837, 49867, 49901, 49939, 49981, 50027, 50077, 50131 
49919, 49921, 49927, 49937   2n^2 - 4n + 49921  4 1 157.9857589  342  = 34.2   49951, 49969, 49991, 50017, 50047, 50081, 50119, 50161, 50207, 50257, 50311 
50087, 50093, 50101, 50111   n^2 + 3n + 50083  2 -1.5 223.7872874  425  = 42.5   50123, 50137, 50153, 50171, 50191, 50213, 50237, 50263, 50291, 50321, 50353 
50153, 50159, 50177, 50207   6n^2 - 12n + 50159  12 1 91.42665549  273  = 27.3   50249, 50303, 50369, 50447, 50537, 50639, 50753, 50879, 51017, 51167, 51329 
50497, 50503, 50513, 50527   2n^2 + 50495  4 0 158.8946192  304  = 30.4   50545, 50567, 50593, 50623, 50657, 50695, 50737, 50783, 50833, 50887, 50945 
51347, 51349, 51361, 51383   5n^2 - 13n + 51355  10 1.3 101.3376041  220  = 22.0   51415, 51457, 51509, 51571, 51643, 51725, 51817, 51919, 52031, 52153, 52285 
51637, 51647, 51659, 51673   n^2 + 7n + 51629  2 -3.5 227.1931997  240  = 24.0   51689, 51707, 51727, 51749, 51773, 51799, 51827, 51857, 51889, 51923, 51959 
52067, 52069, 52081, 52103   5n^2 - 13n + 52075  10 1.3 102.045627  300  = 30.0   52135, 52177, 52229, 52291, 52363, 52445, 52537, 52639, 52751, 52873, 53005 
52147, 52153, 52163, 52177   2n^2 + 52145  4 0 161.4698114  222  = 22.2   52195, 52217, 52243, 52273, 52307, 52345, 52387, 52433, 52483, 52537, 52595 
52249, 52253, 52259, 52267   n^2 + n + 52247  2 -0.5 228.5754799  396  = 39.6   52277, 52289, 52303, 52319, 52337, 52357, 52379, 52403, 52429, 52457, 52487 
52361, 52363, 52369, 52379   2n^2 - 4n + 52363  4 1 161.8038936  319  = 31.9   52393, 52411, 52433, 52459, 52489, 52523, 52561, 52603, 52649, 52699, 52753 
52747, 52757, 52769, 52783   n^2 + 7n + 52739  2 -3.5 229.6230607  544  = 54.4   52799, 52817, 52837, 52859, 52883, 52909, 52937, 52967, 52999, 53033, 53069 
52963, 52967, 52973, 52981   n^2 + n + 52961  2 -0.5 230.1320273  535  = 53.5   52991, 53003, 53017, 53033, 53051, 53071, 53093, 53117, 53143, 53171, 53201 
53089, 53093, 53101, 53113   2n^2 - 2n + 53089  4 0.5 162.9240621  634  = 63.4   53129, 53149, 53173, 53201, 53233, 53269, 53309, 53353, 53401, 53453, 53509 
53773, 53777, 53783, 53791   n^2 + n + 53771  2 -0.5 231.8852087  345  = 34.5   53801, 53813, 53827, 53843, 53861, 53881, 53903, 53927, 53953, 53981, 54011 
53813, 53819, 53831, 53849   3n^2 - 3n + 53813  6 0.5 133.9306413  350  = 35.0   53873, 53903, 53939, 53981, 54029, 54083, 54143, 54209, 54281, 54359, 54443 
53987, 53993, 54001, 54011   n^2 + 3n + 53983  2 -1.5 232.3375777  477  = 47.7   54023, 54037, 54053, 54071, 54091, 54113, 54137, 54163, 54191, 54221, 54253 
55103, 55109, 55117, 55127   n^2 + 3n + 55099  2 -1.5 234.7269691  282  = 28.2   55139, 55153, 55169, 55187, 55207, 55229, 55253, 55279, 55307, 55337, 55369 
55661, 55663, 55667, 55673   n^2 - n + 55661  2 0.5 235.925306  622  = 62.2   55681, 55691, 55703, 55717, 55733, 55751, 55771, 55793, 55817, 55843, 55871 
55663, 55667, 55673, 55681   n^2 + n + 55661  2 -0.5 235.925306  621  = 62.1   55691, 55703, 55717, 55733, 55751, 55771, 55793, 55817, 55843, 55871, 55901 
55667, 55673, 55681, 55691   n^2 + 3n + 55663  2 -1.5 235.925306  620  = 62.0   55703, 55717, 55733, 55751, 55771, 55793, 55817, 55843, 55871, 55901, 55933 
55817, 55819, 55823, 55829   n^2 - n + 55817  2 0.5 236.2556878  478  = 47.8   55837, 55847, 55859, 55873, 55889, 55907, 55927, 55949, 55973, 55999, 56027 
55819, 55823, 55829, 55837   n^2 + n + 55817  2 -0.5 236.2556878  477  = 47.7   55847, 55859, 55873, 55889, 55907, 55927, 55949, 55973, 55999, 56027, 56057 
55933, 55949, 55967, 55987   n^2 + 13n + 55919  2 -6.5 236.3826347  329  = 32.9   56009, 56033, 56059, 56087, 56117, 56149, 56183, 56219, 56257, 56297, 56339 
56437, 56443, 56453, 56467   2n^2 + 56435  4 0 167.9806536  246  = 24.6   56485, 56507, 56533, 56563, 56597, 56635, 56677, 56723, 56773, 56827, 56885 
56501, 56503, 56509, 56519   2n^2 - 4n + 56503  4 1 168.0788505  436  = 43.6   56533, 56551, 56573, 56599, 56629, 56663, 56701, 56743, 56789, 56839, 56893 
56843, 56857, 56873, 56891   n^2 + 11n + 56831  2 -5.5 238.3290792  491  = 49.1   56911, 56933, 56957, 56983, 57011, 57041, 57073, 57107, 57143, 57181, 57221 
57089, 57097, 57107, 57119   n^2 + 5n + 57083  2 -2.5 238.9074088  297  = 29.7   57133, 57149, 57167, 57187, 57209, 57233, 57259, 57287, 57317, 57349, 57383 
57191, 57193, 57203, 57221   4n^2 - 10n + 57197  8 1.25 119.572938  268  = 26.8   57247, 57281, 57323, 57373, 57431, 57497, 57571, 57653, 57743, 57841, 57947 
57709, 57713, 57719, 57727   n^2 + n + 57707  2 -0.5 240.2222929  267  = 26.7   57737, 57749, 57763, 57779, 57797, 57817, 57839, 57863, 57889, 57917, 57947 
57731, 57737, 57751, 57773   4n^2 - 6n + 57733  8 0.75 120.1361207  329  = 32.9   57803, 57841, 57887, 57941, 58003, 58073, 58151, 58237, 58331, 58433, 58543 
58189, 58193, 58199, 58207   n^2 + n + 58187  2 -0.5 241.2192986  422  = 42.2   58217, 58229, 58243, 58259, 58277, 58297, 58319, 58343, 58369, 58397, 58427 
58601, 58603, 58613, 58631   4n^2 - 10n + 58607  8 1.25 121.0379589  386  = 38.6   58657, 58691, 58733, 58783, 58841, 58907, 58981, 59063, 59153, 59251, 59357 
58603, 58613, 58631, 58657   4n^2 - 2n + 58601  8 0.25 121.0379589  386  = 38.6   58691, 58733, 58783, 58841, 58907, 58981, 59063, 59153, 59251, 59357, 59471 
59077, 59083, 59093, 59107   2n^2 + 59075  4 0 171.8647724  222  = 22.2   59125, 59147, 59173, 59203, 59237, 59275, 59317, 59363, 59413, 59467, 59525 
59393, 59399, 59407, 59417   n^2 + 3n + 59389  2 -1.5 243.6939679  426  = 42.6   59429, 59443, 59459, 59477, 59497, 59519, 59543, 59569, 59597, 59627, 59659 
59441, 59443, 59447, 59453   n^2 - n + 59441  2 0.5 243.8047374  419  = 41.9   59461, 59471, 59483, 59497, 59513, 59531, 59551, 59573, 59597, 59623, 59651 
62299, 62303, 62311, 62323   2n^2 - 2n + 62299  4 0.5 176.4915012  348  = 34.8   62339, 62359, 62383, 62411, 62443, 62479, 62519, 62563, 62611, 62663, 62719 
62533, 62539, 62549, 62563   2n^2 + 62531  4 0 176.8205305  436  = 43.6   62581, 62603, 62629, 62659, 62693, 62731, 62773, 62819, 62869, 62923, 62981 
62539, 62549, 62563, 62581   2n^2 + 4n + 62533  4 -1 176.8205305  437  = 43.7   62603, 62629, 62659, 62693, 62731, 62773, 62819, 62869, 62923, 62981, 63043 
63097, 63103, 63113, 63127   2n^2 + 63095  4 0 177.6161592  315  = 31.5   63145, 63167, 63193, 63223, 63257, 63295, 63337, 63383, 63433, 63487, 63545 
63611, 63617, 63629, 63647   3n^2 - 3n + 63611  6 0.5 145.6139302  392  = 39.2   63671, 63701, 63737, 63779, 63827, 63881, 63941, 64007, 64079, 64157, 64241 
64483, 64489, 64499, 64513   2n^2 + 64481  4 0 179.5563978  456  = 45.6   64531, 64553, 64579, 64609, 64643, 64681, 64723, 64769, 64819, 64873, 64931 
64667, 64679, 64693, 64709   n^2 + 9n + 64657  2 -4.5 254.2375857  377  = 37.7   64727, 64747, 64769, 64793, 64819, 64847, 64877, 64909, 64943, 64979, 65017 
64781, 64783, 64793, 64811   4n^2 - 10n + 64787  8 1.25 127.2603139  286  = 28.6   64837, 64871, 64913, 64963, 65021, 65087, 65161, 65243, 65333, 65431, 65537 
64919, 64921, 64927, 64937   2n^2 - 4n + 64921  4 1 180.165202  471  = 47.1   64951, 64969, 64991, 65017, 65047, 65081, 65119, 65161, 65207, 65257, 65311 
64921, 64927, 64937, 64951   2n^2 + 64919  4 0 180.165202  471  = 47.1   64969, 64991, 65017, 65047, 65081, 65119, 65161, 65207, 65257, 65311, 65369 
64927, 64937, 64951, 64969   2n^2 + 4n + 64921  4 -1 180.165202  471  = 47.1   64991, 65017, 65047, 65081, 65119, 65161, 65207, 65257, 65311, 65369, 65431 
65371, 65381, 65393, 65407   n^2 + 7n + 65363  2 -3.5 255.6379275  377  = 37.7   65423, 65441, 65461, 65483, 65507, 65533, 65561, 65591, 65623, 65657, 65693 
65867, 65881, 65899, 65921   2n^2 + 8n + 65857  4 -2 181.4510953  260  = 26.0   65947, 65977, 66011, 66049, 66091, 66137, 66187, 66241, 66299, 66361, 66427 
66529, 66533, 66541, 66553   2n^2 - 2n + 66529  4 0.5 182.3848952  453  = 45.3   66569, 66589, 66613, 66641, 66673, 66709, 66749, 66793, 66841, 66893, 66949 
66533, 66541, 66553, 66569   2n^2 + 2n + 66529  4 -0.5 182.3848952  453  = 45.3   66589, 66613, 66641, 66673, 66709, 66749, 66793, 66841, 66893, 66949, 67009 
66919, 66923, 66931, 66943   2n^2 - 2n + 66919  4 0.5 182.9186978  478  = 47.8   66959, 66979, 67003, 67031, 67063, 67099, 67139, 67183, 67231, 67283, 67339 
67619, 67631, 67651, 67679   4n^2 + 67615  8 0 130.0144223  277  = 27.7   67715, 67759, 67811, 67871, 67939, 68015, 68099, 68191, 68291, 68399, 68515 
68207, 68209, 68213, 68219   n^2 - n + 68207  2 0.5 261.1642204  410  = 41.0   68227, 68237, 68249, 68263, 68279, 68297, 68317, 68339, 68363, 68389, 68417 
68209, 68213, 68219, 68227   n^2 + n + 68207  2 -0.5 261.1642204  410  = 41.0   68237, 68249, 68263, 68279, 68297, 68317, 68339, 68363, 68389, 68417, 68447 
68771, 68777, 68791, 68813   4n^2 - 6n + 68773  8 0.75 131.1208889  330  = 33.0   68843, 68881, 68927, 68981, 69043, 69113, 69191, 69277, 69371, 69473, 69583 
68897, 68899, 68903, 68909   n^2 - n + 68897  2 0.5 262.4819041  460  = 46.0   68917, 68927, 68939, 68953, 68969, 68987, 69007, 69029, 69053, 69079, 69107 
68899, 68903, 68909, 68917   n^2 + n + 68897  2 -0.5 262.4819041  459  = 45.9   68927, 68939, 68953, 68969, 68987, 69007, 69029, 69053, 69079, 69107, 69137 
68903, 68909, 68917, 68927   n^2 + 3n + 68899  2 -1.5 262.4819041  458  = 45.8   68939, 68953, 68969, 68987, 69007, 69029, 69053, 69079, 69107, 69137, 69169 
69191, 69193, 69197, 69203   n^2 - n + 69191  2 0.5 263.0413466  522  = 52.2   69211, 69221, 69233, 69247, 69263, 69281, 69301, 69323, 69347, 69373, 69401 
69233, 69239, 69247, 69257   n^2 + 3n + 69229  2 -1.5 263.109768  417  = 41.7   69269, 69283, 69299, 69317, 69337, 69359, 69383, 69409, 69437, 69467, 69499 
69463, 69467, 69473, 69481   n^2 + n + 69461  2 -0.5 263.5540741  320  = 32.0   69491, 69503, 69517, 69533, 69551, 69571, 69593, 69617, 69643, 69671, 69701 
69467, 69473, 69481, 69491   n^2 + 3n + 69463  2 -1.5 263.5540741  320  = 32.0   69503, 69517, 69533, 69551, 69571, 69593, 69617, 69643, 69671, 69701, 69733 
69929, 69931, 69941, 69959   4n^2 - 10n + 69935  8 1.25 132.2202235  339  = 33.9   69985, 70019, 70061, 70111, 70169, 70235, 70309, 70391, 70481, 70579, 70685 
70001, 70003, 70009, 70019   2n^2 - 4n + 70003  4 1 187.0842056  434  = 43.4   70033, 70051, 70073, 70099, 70129, 70163, 70201, 70243, 70289, 70339, 70393 
70621, 70627, 70639, 70657   3n^2 - 3n + 70621  6 0.5 153.4277789  392  = 39.2   70681, 70711, 70747, 70789, 70837, 70891, 70951, 71017, 71089, 71167, 71251 
71011, 71023, 71039, 71059   2n^2 + 6n + 71003  4 -1.5 188.4124465  315  = 31.5   71083, 71111, 71143, 71179, 71219, 71263, 71311, 71363, 71419, 71479, 71543 
71143, 71147, 71153, 71161   n^2 + n + 71141  2 -0.5 266.7222338  260  = 26.0   71171, 71183, 71197, 71213, 71231, 71251, 71273, 71297, 71323, 71351, 71381 
71327, 71329, 71333, 71339   n^2 - n + 71327  2 0.5 267.0706835  317  = 31.7   71347, 71357, 71369, 71383, 71399, 71417, 71437, 71459, 71483, 71509, 71537 
71411, 71413, 71419, 71429   2n^2 - 4n + 71413  4 1 188.9589903  343  = 34.3   71443, 71461, 71483, 71509, 71539, 71573, 71611, 71653, 71699, 71749, 71803 
72269, 72271, 72277, 72287   2n^2 - 4n + 72271  4 1 190.0907678  369  = 36.9   72301, 72319, 72341, 72367, 72397, 72431, 72469, 72511, 72557, 72607, 72661 
72671, 72673, 72679, 72689   2n^2 - 4n + 72673  4 1 190.6187294  329  = 32.9   72703, 72721, 72743, 72769, 72799, 72833, 72871, 72913, 72959, 73009, 73063 
73361, 73363, 73369, 73379   2n^2 - 4n + 73363  4 1 191.5215393  431  = 43.1   73393, 73411, 73433, 73459, 73489, 73523, 73561, 73603, 73649, 73699, 73753 
73417, 73421, 73433, 73453   4n^2 - 8n + 73421  8 1 135.477858  521  = 52.1   73481, 73517, 73561, 73613, 73673, 73741, 73817, 73901, 73993, 74093, 74201 
73547, 73553, 73561, 73571   n^2 + 3n + 73543  2 -1.5 271.1839781  457  = 45.7   73583, 73597, 73613, 73631, 73651, 73673, 73697, 73723, 73751, 73781, 73813 
73553, 73561, 73571, 73583   n^2 + 5n + 73547  2 -2.5 271.1839781  457  = 45.7   73597, 73613, 73631, 73651, 73673, 73697, 73723, 73751, 73781, 73813, 73847 
73583, 73589, 73597, 73607   n^2 + 3n + 73579  2 -1.5 271.2503456  228  = 22.8   73619, 73633, 73649, 73667, 73687, 73709, 73733, 73759, 73787, 73817, 73849 
73943, 73951, 73961, 73973   n^2 + 5n + 73937  2 -2.5 271.9020964  293  = 29.3   73987, 74003, 74021, 74041, 74063, 74087, 74113, 74141, 74171, 74203, 74237 
74159, 74161, 74167, 74177   2n^2 - 4n + 74161  4 1 192.5603801  369  = 36.9   74191, 74209, 74231, 74257, 74287, 74321, 74359, 74401, 74447, 74497, 74551 
74201, 74203, 74209, 74219   2n^2 - 4n + 74203  4 1 192.6149008  406  = 40.6   74233, 74251, 74273, 74299, 74329, 74363, 74401, 74443, 74489, 74539, 74593 
75227, 75239, 75253, 75269   n^2 + 9n + 75217  2 -4.5 274.2202582  537  = 53.7   75287, 75307, 75329, 75353, 75379, 75407, 75437, 75469, 75503, 75539, 75577 
75323, 75329, 75337, 75347   n^2 + 3n + 75319  2 -1.5 274.4389732  354  = 35.4   75359, 75373, 75389, 75407, 75427, 75449, 75473, 75499, 75527, 75557, 75589 
76829, 76831, 76837, 76847   2n^2 - 4n + 76831  4 1 195.9961734  297  = 29.7   76861, 76879, 76901, 76927, 76957, 76991, 77029, 77071, 77117, 77167, 77221 
77237, 77239, 77243, 77249   n^2 - n + 77237  2 0.5 277.915005  506  = 50.6   77257, 77267, 77279, 77293, 77309, 77327, 77347, 77369, 77393, 77419, 77447 
77719, 77723, 77731, 77743   2n^2 - 2n + 77719  4 0.5 197.1274968  359  = 35.9   77759, 77779, 77803, 77831, 77863, 77899, 77939, 77983, 78031, 78083, 78139 
78341, 78347, 78367, 78401   7n^2 - 15n + 78349  14 1.071428571 105.7901996  363  = 36.3   78449, 78511, 78587, 78677, 78781, 78899, 79031, 79177, 79337, 79511, 79699 
78479, 78487, 78497, 78509   n^2 + 5n + 78473  2 -2.5 280.1191711  435  = 43.5   78523, 78539, 78557, 78577, 78599, 78623, 78649, 78677, 78707, 78739, 78773 
78577, 78583, 78593, 78607   2n^2 + 78575  4 0 198.2107464  231  = 23.1   78625, 78647, 78673, 78703, 78737, 78775, 78817, 78863, 78913, 78967, 79025 
79229, 79231, 79241, 79259   4n^2 - 10n + 79235  8 1.25 140.7380101  209  = 20.9   79285, 79319, 79361, 79411, 79469, 79535, 79609, 79691, 79781, 79879, 79985 
79349, 79357, 79367, 79379   n^2 + 5n + 79343  2 -2.5 281.6678008  325  = 32.5   79393, 79409, 79427, 79447, 79469, 79493, 79519, 79547, 79577, 79609, 79643 
79357, 79367, 79379, 79393   n^2 + 7n + 79349  2 -3.5 281.6678008  325  = 32.5   79409, 79427, 79447, 79469, 79493, 79519, 79547, 79577, 79609, 79643, 79679 
79427, 79433, 79451, 79481   6n^2 - 12n + 79433  12 1 115.0557836  399  = 39.9   79523, 79577, 79643, 79721, 79811, 79913, 80027, 80153, 80291, 80441, 80603 
79811, 79813, 79817, 79823   n^2 - n + 79811  2 0.5 282.5079645  539  = 53.9   79831, 79841, 79853, 79867, 79883, 79901, 79921, 79943, 79967, 79993, 80021 
79973, 79979, 79987, 79997   n^2 + 3n + 79969  2 -1.5 282.7839281  532  = 53.2   80009, 80023, 80039, 80057, 80077, 80099, 80123, 80149, 80177, 80207, 80239 
80369, 80387, 80407, 80429   n^2 + 15n + 80353  2 -7.5 283.3668117  256  = 25.6   80453, 80479, 80507, 80537, 80569, 80603, 80639, 80677, 80717, 80759, 80803 
80777, 80779, 80783, 80789   n^2 - n + 80777  2 0.5 284.2125085  498  = 49.8   80797, 80807, 80819, 80833, 80849, 80867, 80887, 80909, 80933, 80959, 80987 
81937, 81943, 81953, 81967   2n^2 + 81935  4 0 202.4042984  314  = 31.4   81985, 82007, 82033, 82063, 82097, 82135, 82177, 82223, 82273, 82327, 82385 
82351, 82361, 82373, 82387   n^2 + 7n + 82343  2 -3.5 286.9333546  373  = 37.3   82403, 82421, 82441, 82463, 82487, 82513, 82541, 82571, 82603, 82637, 82673 
83399, 83401, 83407, 83417   2n^2 - 4n + 83401  4 1 204.2045543  599  = 59.9   83431, 83449, 83471, 83497, 83527, 83561, 83599, 83641, 83687, 83737, 83791 
83903, 83911, 83921, 83933   n^2 + 5n + 83897  2 -2.5 289.6389994  336  = 33.6   83947, 83963, 83981, 84001, 84023, 84047, 84073, 84101, 84131, 84163, 84197 
84221, 84223, 84229, 84239   2n^2 - 4n + 84223  4 1 205.2084306  375  = 37.5   84253, 84271, 84293, 84319, 84349, 84383, 84421, 84463, 84509, 84559, 84613 
84521, 84523, 84533, 84551   4n^2 - 10n + 84527  8 1.25 145.362263  436  = 43.6   84577, 84611, 84653, 84703, 84761, 84827, 84901, 84983, 85073, 85171, 85277 
84809, 84811, 84827, 84857   7n^2 - 19n + 84821  14 1.357142857 110.0701771  227  = 22.7   84901, 84959, 85031, 85117, 85217, 85331, 85459, 85601, 85757, 85927, 86111 
85513, 85517, 85523, 85531   n^2 + n + 85511  2 -0.5 292.4222119  462  = 46.2   85541, 85553, 85567, 85583, 85601, 85621, 85643, 85667, 85693, 85721, 85751 
86239, 86243, 86249, 86257   n^2 + n + 86237  2 -0.5 293.6609439  458  = 45.8   86267, 86279, 86293, 86309, 86327, 86347, 86369, 86393, 86419, 86447, 86477 
86461, 86467, 86477, 86491   2n^2 + 86459  4 0 207.9170508  398  = 39.8   86509, 86531, 86557, 86587, 86621, 86659, 86701, 86747, 86797, 86851, 86909 
86951, 86959, 86969, 86981   n^2 + 5n + 86945  2 -2.5 294.8537773  457  = 45.7   86995, 87011, 87029, 87049, 87071, 87095, 87121, 87149, 87179, 87211, 87245 
87317, 87323, 87337, 87359   4n^2 - 6n + 87319  8 0.75 147.7470389  279  = 27.9   87389, 87427, 87473, 87527, 87589, 87659, 87737, 87823, 87917, 88019, 88129 
87793, 87797, 87803, 87811   n^2 + n + 87791  2 -0.5 296.2950388  321  = 32.1   87821, 87833, 87847, 87863, 87881, 87901, 87923, 87947, 87973, 88001, 88031 
88867, 88873, 88883, 88897   2n^2 + 88865  4 0 210.79018  343  = 34.3   88915, 88937, 88963, 88993, 89027, 89065, 89107, 89153, 89203, 89257, 89315 
90281, 90289, 90313, 90353   8n^2 - 16n + 90289  16 1 106.231469  382  = 38.2   90409, 90481, 90569, 90673, 90793, 90929, 91081, 91249, 91433, 91633, 91849 
90641, 90647, 90659, 90677   3n^2 - 3n + 90641  6 0.5 173.8200698  401  = 40.1   90701, 90731, 90767, 90809, 90857, 90911, 90971, 91037, 91109, 91187, 91271 
91571, 91573, 91577, 91583   n^2 - n + 91571  2 0.5 302.6065928  464  = 46.4   91591, 91601, 91613, 91627, 91643, 91661, 91681, 91703, 91727, 91753, 91781 
91573, 91577, 91583, 91591   n^2 + n + 91571  2 -0.5 302.6065928  463  = 46.3   91601, 91613, 91627, 91643, 91661, 91681, 91703, 91727, 91753, 91781, 91811 
92233, 92237, 92243, 92251   n^2 + n + 92231  2 -0.5 303.6951597  321  = 32.1   92261, 92273, 92287, 92303, 92321, 92341, 92363, 92387, 92413, 92441, 92471 
92243, 92251, 92269, 92297   5n^2 - 7n + 92245  10 0.7 135.8252922  251  = 25.1   92335, 92383, 92441, 92509, 92587, 92675, 92773, 92881, 92999, 93127, 93265 
92639, 92641, 92647, 92657   2n^2 - 4n + 92641  4 1 215.2196552  460  = 46.0   92671, 92689, 92711, 92737, 92767, 92801, 92839, 92881, 92927, 92977, 93031 
92693, 92699, 92707, 92717   n^2 + 3n + 92689  2 -1.5 304.4449868  300  = 30.0   92729, 92743, 92759, 92777, 92797, 92819, 92843, 92869, 92897, 92927, 92959 
93133, 93139, 93151, 93169   3n^2 - 3n + 93133  6 0.5 176.1933124  393  = 39.3   93193, 93223, 93259, 93301, 93349, 93403, 93463, 93529, 93601, 93679, 93763 
93251, 93253, 93257, 93263   n^2 - n + 93251  2 0.5 305.3698577  434  = 43.4   93271, 93281, 93293, 93307, 93323, 93341, 93361, 93383, 93407, 93433, 93461 
93319, 93323, 93329, 93337   n^2 + n + 93317  2 -0.5 305.4779043  275  = 27.5   93347, 93359, 93373, 93389, 93407, 93427, 93449, 93473, 93499, 93527, 93557 
93491, 93493, 93497, 93503   n^2 - n + 93491  2 0.5 305.7625713  444  = 44.4   93511, 93521, 93533, 93547, 93563, 93581, 93601, 93623, 93647, 93673, 93701 
95531, 95539, 95549, 95561   n^2 + 5n + 95525  2 -2.5 309.0610781  339  = 33.9   95575, 95591, 95609, 95629, 95651, 95675, 95701, 95729, 95759, 95791, 95825 
95561, 95569, 95581, 95597   2n^2 + 2n + 95557  4 -0.5 218.5823643  222  = 22.2   95617, 95641, 95669, 95701, 95737, 95777, 95821, 95869, 95921, 95977, 96037 
95713, 95717, 95723, 95731   n^2 + n + 95711  2 -0.5 309.3715404  287  = 28.7   95741, 95753, 95767, 95783, 95801, 95821, 95843, 95867, 95893, 95921, 95951 
96149, 96157, 96167, 96179   n^2 + 5n + 96143  2 -2.5 310.0592685  397  = 39.7   96193, 96209, 96227, 96247, 96269, 96293, 96319, 96347, 96377, 96409, 96443 
97169, 97171, 97177, 97187   2n^2 - 4n + 97171  4 1 220.4189193  320  = 32.0   97201, 97219, 97241, 97267, 97297, 97331, 97369, 97411, 97457, 97507, 97561 
97367, 97369, 97373, 97379   n^2 - n + 97367  2 0.5 312.0364562  523  = 52.3   97387, 97397, 97409, 97423, 97439, 97457, 97477, 97499, 97523, 97549, 97577 
97379, 97381, 97387, 97397   2n^2 - 4n + 97381  4 1 220.6569736  362  = 36.2   97411, 97429, 97451, 97477, 97507, 97541, 97579, 97621, 97667, 97717, 97771 
97967, 97973, 97987, 98009   4n^2 - 6n + 97969  8 0.75 156.4982029  372  = 37.2   98039, 98077, 98123, 98177, 98239, 98309, 98387, 98473, 98567, 98669, 98779 
99607, 99611, 99623, 99643   4n^2 - 8n + 99611  8 1 157.8028834  261  = 26.1   99671, 99707, 99751, 99803, 99863, 99931, 100007, 100091, 100183, 100283, 100391 
99707, 99709, 99713, 99719   n^2 - n + 99707  2 0.5 315.7637566  369  = 36.9   99727, 99737, 99749, 99763, 99779, 99797, 99817, 99839, 99863, 99889, 99917 

 

 
© 2007-2008 Michael M. Ross