The High Primality of Prime-Derived Quadratic Sequences

An analysis of the first 100 Proximate-Prime Polynomials* for n = 0 to 1000

Green column shows the density of primes in the first 1000 terms of the quadratic expression.

Use QTest to generate complete sequences by entering the 4 proximate primes from a row in this table.

Proximate Primes	Quadratic	Type of Root	Roots	Primes % (n=0 to 1000)	Prime Sequence (First 10)	Perf. Sqrs. (n=0 to 1000)
17, 19, 23, 29	n^2 - n + 17	Complex	0.5+/-4.09267638593623i	366 Primes = 36.60%	17, 19, 23, 29, 37, 47, 59, 73, 89, 107	289
31, 37, 41, 43	-1n^2 + 9n + 23	Real	-2.07647321898295 +11.07647321898295	373 Primes = 37.30%	31, 37, 41, 43, 43, 41, 37, 31, 23, 13	1, -1849
41, 43, 47, 53	n^2 - n + 41	Complex	0.5+/-6.38357266740185i	582 Primes = 58.20%	41, 43, 47, 53, 61, 71, 83, 97, 113, 131	1681
61, 67, 71, 73	-1n^2 + 9n + 53	Real	-4.05862138431185 +13.05862138431185	436 Primes = 43.60%	61, 67, 71, 73, 73, 71, 67, 61, 53, 43	1, -5329
79, 83, 89, 97	n^2 + n + 77	Complex	-0.5+/-8.7607077339676i	249 Primes = 24.90%	79, 83, 89, 97, 107, 119, 133, 149, 167, 187	5929
227, 229, 233, 239	n^2 - n + 227	Complex	0.5+/-15.0582203463756i	447 Primes = 44.70%	227, 229, 233, 239, 247, 257, 269, 283, 299, 317	51529
271, 277, 281, 283	-1n^2 + 9n + 263	Real	-12.33003267970685 +21.33003267970685	511 Primes = 51.10%	271, 277, 281, 283, 283, 281, 277, 271, 263, 253	-529, -80089
347, 349, 353, 359	n^2 - n + 347	Complex	0.5+/-18.62122444953605i	419 Primes = 41.90%	347, 349, 353, 359, 367, 377, 389, 403, 419, 437	529, 120409
349, 353, 359, 367	n^2 + n + 347	Complex	-0.5+/-18.62122444953605i	419 Primes = 41.90%	349, 353, 359, 367, 377, 389, 403, 419, 437, 457	529, 120409
379, 383, 389, 405	n^2 + n + 377	Complex	-0.5+/-19.41004894378165i	418 Primes = 41.80%	379, 383, 389, 397, 407, 419, 433, 449, 467, 487	1369, 142129
439, 443, 449, 457	n^2 + n + 437	Complex	-0.5+/-20.89856454400635i	360 Primes = 36.00%	439, 443, 449, 457, 467, 479, 493, 509, 527, 547	190969
467, 479, 487, 491	-2n^2 + 18n + 451	Real	-11.17641540659088 +20.17641540659088	478 Primes = 47.80%	467, 479, 487, 491, 491, 487, 479, 467, 451, 431	-121, -1369, -10609, -54289, -368449, -1852321
569, 571, 577, 587	2n^2 - 4n + 571	Complex	1+/-16.867127793433i	350 Primes = 35.00%	569, 571, 577, 587, 601, 619, 641, 667, 697, 731	961, 1369, 22201, 36481, 744769, 1229881
607, 613, 617, 619	-1n^2 + 9n + 599	Real	-20.3847342762586 +29.3847342762586	549 Primes = 54.90%	607, 613, 617, 619, 619, 617, 613, 607, 599, 589	529, -383161
641, 643, 647, 653	n^2 - n + 641	Complex	0.5+/-25.3130401176943i	369 Primes = 36.90%	641, 643, 647, 653, 661, 671, 683, 697, 713, 731	3721, 410881
673, 677, 683, 691	n^2 + n + 671	Complex	-0.5+/-25.89884167293975i	453 Primes = 45.30%	673, 677, 683, 691, 701, 713, 727, 743, 761, 781	450241
677, 683, 691, 701	n^2 + 3n + 673	Complex	-1.5+/-25.89884167293975i	455 Primes = 45.50%	677, 683, 691, 701, 713, 727, 743, 761, 781, 803	450241
709, 719, 727, 733	-1n^2 + 13n + 697	Real	-20.68915224864505 +33.68915224864505	349 Primes = 34.90%	709, 719, 727, 733, 737, 739, 739, 737, 733, 727	529, -546121
743, 751, 757, 761	-1n^2 + 11n + 733	Real	-22.1269795670826 +33.1269795670826	459 Primes = 45.90%	743, 751, 757, 761, 763, 763, 761, 757, 751, 743	-49, -582169
1031, 1033, 1039, 1049	2n^2 - 4n + 1033	Complex	1+/-22.70462507948545i	471 Primes = 47.10%	1031, 1033, 1039, 1049, 1063, 1081, 1103, 1129, 1159, 1193	1369, 3481, 26569, 100489, 885481
1091, 1093, 1097, 1103	n^2 - n + 1091	Complex	0.5+/-33.0265045077435i	317 Primes = 31.70%	1091, 1093, 1097, 1103, 1111, 1121, 1133, 1147, 1163, 1181
1277, 1279, 1283, 1289	n^2 - n + 1277	Complex	0.5+/-35.73163864140575i	459 Primes = 45.90%	1277, 1279, 1283, 1289, 1297, 1307, 1319, 1333, 1349, 1367
1291, 1297, 1301, 1303	-1n^2 + 9n + 1283	Real	-31.6005540123694 +40.6005540123694	449 Primes = 44.90%	1291, 1297, 1301, 1303, 1303, 1301, 1297, 1291, 1283, 1273	961, 841, -9409
1427, 1429, 1433, 1439	n^2 - n + 1427	Complex	0.5+/-37.77234438051205i	426 Primes = 42.60%	1427, 1429, 1433, 1439, 1447, 1457, 1469, 1483, 1499, 1517	12769
1429, 1433, 1439, 1447	n^2 + n + 1427	Complex	-0.5+/-37.77234438051205i	426 Primes = 42.60%	1429, 1433, 1439, 1447, 1457, 1469, 1483, 1499, 1517, 1537	12769
1487, 1489, 1493, 1499	n^2 - n + 1487	Complex	0.5+/-38.55839726959615i	420 Primes = 42.00%	1487, 1489, 1493, 1499, 1507, 1517, 1529, 1543, 1559, 1577	6889
1549, 1553, 1559, 1567	n^2 + n + 1547	Complex	-0.5+/-39.32874266996085i	265 Primes = 26.50%	1549, 1553, 1559, 1567, 1577, 1589, 1603, 1619, 1637, 1657	5329
1607, 1609, 1613, 1619,	n^2 - n + 1607	Complex	0.5+/-40.0842861979604i	388 Primes = 38.80%	1607, 1609, 1613, 1619, 1627, 1637, 1649, 1663, 1679, 1697
1619, 1621, 1627, 1637	2n^2 - 4n + 1621	Complex	1+/-28.4517134809135i	402 Primes = 40.20%	1619, 1621, 1627, 1637, 1651, 1669, 1691, 1717, 1747, 1781
1657, 1663, 1667, 1669	-1n^2 + 9n + 1649	Real	-36.35645603818325 +45.35645603818325	486 Primes = 48.60%	1657, 1663, 1667, 1669, 1669, 1667, 1663, 1657, 1649, 1639	-22201
1723, 1733, 1741, 1747	-1n^2 + 13n + 1711	Real	-35.3718282380887 +48.3718282380887	479 Primes = 47.90%	1723, 1733, 1741, 1747, 1751, 1753, 1753, 1751, 1747, 1741	1681
1777, 1783, 1787, 1789	-1n^2 + 9n + 1769	Real	-37.79952718411875 +46.79952718411875	494 Primes = 49.40%	1777, 1783, 1787, 1789, 1789, 1787, 1783, 1777, 1769, 1759	1369, 529, -10201
1861, 1867, 1871, 1873	-1n^2 + 9n + 1853	Real	-38.78105821257145 +47.78105821257145	414 Primes = 41.40%	1861, 1867, 1871, 1873, 1873, 1871, 1867, 1861, 1853, 1843	-289
1979, 1987, 1993, 1997	-1n^2 + 11n + 1969	Real	-39.2129735088151 +50.2129735088151	405 Primes = 40.50%	1979, 1987, 1993, 1997, 1999, 1999, 1997, 1993, 1987, 1979	-32041
1987, 1993, 1997, 1999	-1n^2 + 9n + 1979	Real	-40.2129735088151 +49.2129735088151	403 Primes = 40.30%	1987, 1993, 1997, 1999, 1999, 1997, 1993, 1987, 1979, 1969	-32041
2039, 2053, 2063, 2069	-2n^2 + 20n + 2021	Real	-27.17918581940825 +37.17918581940825	399 Primes = 39.90%	2039, 2053, 2063, 2069, 2071, 2069, 2063, 2053, 2039, 2021
2131, 2137, 2141, 2143	-1n^2 + 9n + 2123	Real	-41.79524813628285 +50.79524813628285	419 Primes = 41.90%	2131, 2137, 2141, 2143, 2143, 2141, 2137, 2131, 2123, 2113	1681
2203, 2207, 2213, 2221	n^2 + n + 2201	Complex	-0.5+/-46.9121519438194i	459 Primes = 45.90%	2203, 2207, 2213, 2221, 2231, 2243, 2257, 2273, 2291, 2311
2371, 2377, 2381, 2383	-1n^2 + 9n + 2363	Real	-44.31854155953455 +53.31854155953455	439 Primes = 43.90%	2371, 2377, 2381, 2383, 2383, 2381, 2377, 2371, 2363, 2353	1681
2459, 2467, 2473, 2477	-1n^2 + 11n + 2449	Real	-44.2920676413422 +55.2920676413422	444 Primes = 44.40%	2459, 2467, 2473, 2477, 2479, 2479, 2477, 2473, 2467, 2459	-1681
2477, 2503, 2521, 2531	-4n^2 + 38n + 2443	Real	-20.41570086447025 +29.91570086447025	281 Primes = 28.10%	2477, 2503, 2521, 2531, 2533, 2527, 2513, 2491, 2461, 2423
2557, 2579, 2591, 2593	-5n^2 + 37n + 2525	Real	-19.0747667386518 +26.4747667386518	197 Primes = 19.70%	2557, 2579, 2591, 2593, 2585, 2567, 2539, 2501, 2453, 2395	-121
2677, 2683, 2687, 2689	-1n^2 + 9n + 2669	Real	-47.357979135327 +56.357979135327	504 Primes = 50.40%	2677, 2683, 2687, 2689, 2689, 2687, 2683, 2677, 2669, 2659	-6241
2687, 2689, 2693, 2699	n^2 - n + 2687	Complex	0.5+/-51.8338692362435i	359 Primes = 35.90%	2687, 2689, 2693, 2699, 2707, 2717, 2729, 2743, 2759, 2777	61009
2689, 2693, 2699	n^2 + n + 2687	Complex	-0.5+/-51.8338692362435i	355 Primes = 35.50%	2689, 2693, 2699, 2707, 2717, 2729, 2743, 2759, 2777, 2797	61009
2711, 2713, 2719, 2729	2n^2 - 4n + 2713	Complex	1+/-36.81711558501025i	328 Primes = 32.80%	2711, 2713, 2719, 2729, 2743, 2761, 2783, 2809, 2839, 2873	2809, 17161, 34969, 537289, 1142761
2791, 2797, 2801, 2803	-1n^2 + 9n + 2783	Real	-48.44572692862 +57.44572692862	493 Primes = 49.30%	2791, 2797, 2801, 2803, 2803, 2801, 2797, 2791, 2783, 2773	1681
2833, 2837, 2843, 2851	n^2 + n + 2831	Complex	-0.5+/-53.204793017171i	333 Primes = 33.30%	2833, 2837, 2843, 2851, 2861, 2873, 2887, 2903, 2921, 2941	3481, 48841
2843, 2851, 2857, 2861	-1n^2 + 11n + 2833	Real	-48.009344978237 +59.009344978237	384 Primes = 38.40%	2843, 2851, 2857, 2861, 2863, 2863, 2861, 2857, 2851, 2843	2401, 1, -47089
2903, 2909, 2917, 2927	n^2 + 3n + 2899	Complex	-1.5+/-53.82146411981i	352 Primes = 35.20%	2903, 2909, 2917, 2927, 2939, 2953, 2969, 2987, 3007, 3029
2909, 2917, 2927, 2939	n^2 + 5n + 2903	Complex	-2.5+/-53.82146411981i	356 Primes = 35.60%	2909, 2917, 2927, 2939, 2953, 2969, 2987, 3007, 3029, 3053
2917, 2927, 2939, 2953	n^2 + 7n + 2909	Complex	-3.5+/-53.82146411981i	361 Primes = 36.10%	2917, 2927, 2939, 2953, 2969, 2987, 3007, 3029, 3053, 3079
3037, 3041, 3049, 3061	2n^2 - 2n + 3037	Complex	0.5+/-38.964727639238i	409 Primes = 40.90%	3037, 3041, 3049, 3061, 3077, 3097, 3121, 3149, 3181, 3217	3721, 11881, 66049, 351649
3527, 3529, 3533, 3539	n^2 - n + 3527	Complex	0.5+/-59.38644626512i	479 Primes = 47.90%	3527, 3529, 3533, 3539, 3547, 3557, 3569, 3583, 3599, 3617
3539, 3541, 3547, 3557	2n^2 - 4n + 3541	Complex	1+/-42.0654252326065i	409 Primes = 40.90%	3539, 3541, 3547, 3557, 3571, 3589, 3611, 3637, 3667, 3701
3613, 3617, 3623, 3631	n^2 + n + 3611	Complex	-0.5+/-60.089516556551i	436 Primes = 43.60%	3613, 3617, 3623, 3631, 3641, 3653, 3667, 3683, 3701, 3721	3721, 78961, 109561
3709, 3719, 3727, 3733	-1n^2 + 13n + 3697	Real	-54.6494071925475 +67.6494071925475	445 Primes = 44.50%	3709, 3719, 3727, 3733, 3737, 3739, 3739, 3737, 3733, 3727	2809
3917, 3919, 3923, 3929	n^2 - n + 3917	Complex	0.5+/-62.583943627739i	489 Primes = 48.90%	3917, 3919, 3923, 3929, 3937, 3947, 3959, 3973, 3989, 4007
3967, 3989, 4001, 4003	-5n^2 + 37n + 3935	Real	-24.5964662104652 +31.9964662104652	265 Primes = 26.50%	3967, 3989, 4001, 4003, 3995, 3977, 3949, 3911, 3863, 3805	-1, -289, -10201, -19321, -4879681
4001, 4003, 4007, 4013	n^2 - n + 4001	Complex	0.5+/-63.251482196072i	451 Primes = 45.10%	4001, 4003, 4007, 4013, 4021, 4031, 4043, 4057, 4073, 4091	96721
4127, 4129, 4133, 4139	n^2 - n + 4127	Complex	0.5+/-64.2397851802135i	278 Primes = 27.80%	4127, 4129, 4133, 4139, 4147, 4157, 4169, 4183, 4199, 4217	61009
4201, 4211, 4217, 4219	-2n^2 + 16n + 4187	Real	-41.92929348465975 +49.92929348465975	309 Primes = 30.90%	4201, 4211, 4217, 4219, 4217, 4211, 4201, 4187, 4169, 4147	169
4243, 4253, 4259	-2n^2 + 16n + 4229	Real	-42.157339611377 +50.157339611377	446 Primes = 44.60%	4201, 4211, 4217, 4219, 4259, 4253, 4243, 4229, 4211, 4189
4339, 4349, 4357, 4363	-1n^2 + 13n + 4327	Real	-59.6003025711685 +72.6003025711685	458 Primes = 45.80%	4339, 4349, 4357, 4363, 4367, 4369, 4369, 4367, 4363, 4357	2809
4507, 4513, 4517, 4519	-1n^2 + 9n + 4499	Real	-62.725367235888 +71.725367235888	418 Primes = 41.80%	4507, 4513, 4517, 4519, 4519, 4517, 4513, 4507, 4499, 4489	4489
4637, 4639, 4643, 4649	n^2 - n + 4637	Complex	0.5+/-68.093685463485i	409 Primes = 40.90%	4637, 4639, 4643, 4649, 4657, 4667, 4679, 4693, 4709, 4727	76729
4787, 4789, 4793, 4799	n^2 - n + 4787	Complex	0.5+/-69.1863425829115i	374 Primes = 37.40%	4787, 4789, 4793, 4799, 4807, 4817, 4829, 4843, 4859, 4877	16129
4931, 4933, 4937, 4943	n^2 - n + 4931	Complex	0.5+/-70.2192993414205i	503 Primes = 50.30%	4931, 4933, 4937, 4943, 4951, 4961, 4973, 4987, 5003, 5021	5041, 203401
4933, 4937, 4943, 4951	n^2 + n + 4931	Complex	-0.5+/-70.2192993414205i	503 Primes = 50.30%	4933, 4937, 4943, 4951, 4961, 4973, 4987, 5003, 5021, 5041	5041, 203401
5023, 5039, 5051, 5059	-2n^2 + 22n + 5003	Real	-44.81649828833475 +55.81649828833475	454 Primes = 45.40%	5023, 5039, 5051, 5059, 5063, 5063, 5059, 5051, 5039, 5023
5399, 5407, 5413, 5417	-1n^2 + 11n + 5389	Real	-68.115555421392 +79.115555421392	492 Primes = 49.20%	5399, 5407, 5413, 5417, 5419, 5419, 5417, 5413, 5407, 5399	5329, 4489, -7921
5407, 5413, 5417, 5419	-1n^2 + 9n + 5399	Real	-69.115555421392 +78.115555421392	493 Primes = 49.30%	5407, 5413, 5417, 5419, 5419, 5417, 5413, 5407, 5399, 5389	5329, 4489, -7921
5431, 5437, 5441, 5443	-1n^2 + 9n + 5423	Real	-69.278384368323 +78.278384368323	349 Primes = 34.90%	5431, 5437, 5441, 5443, 5443, 5441, 5437, 5431, 5423, 5413	3721
5641, 5647, 5651, 5653	-1n^2 + 9n + 5633	Real	-70.688097462298 +79.688097462298	482 Primes = 48.20%	5641, 5647, 5651, 5653, 5653, 5651, 5647, 5641, 5633, 5623	961
6029, 6037, 6043, 6047	-1n^2 + 11n + 6019	Real	-72.276924598495 +83.276924598495	406 Primes = 40.60%	6029, 6037, 6043, 6047, 6049, 6049, 6047, 6043, 6037, 6029	4489
6203, 6211, 6217, 6221	-1n^2 + 11n + 6193	Real	-73.387578236374 +84.387578236374	409 Primes = 40.90%	6203, 6211, 6217, 6221, 6223, 6223, 6221, 6217, 6211, 6203	-4489, -37249, -316969
6269, 6271, 6277, 6287	2n^2 - 4n + 6271	Complex	1+/-55.9866055409685i	466 Primes = 46.60%	6269, 6271, 6277, 6287, 6301, 6319, 6341, 6367, 6397, 6431
6343, 6353, 6359, 6361	-2n^2 + 16n + 6329	Real	-52.395921838374 +60.395921838374	454 Primes = 45.40%	6343, 6353, 6359, 6361, 6359, 6353, 6343, 6329, 6311, 6289	529, -3721, -10201, -218089, -444889
6553, 6563, 6569, 6571	-2n^2 + 16n + 6539	Real	-53.319281223686 +61.319281223686	377 Primes = 37.70%	6553, 6563, 6569, 6571, 6569, 6563, 6553, 6539, 6521, 6499	1369
6701, 6703, 6709, 6719	2n^2 - 4n + 6703	Complex	1+/-57.8835036949215i	429 Primes = 42.90%	6701, 6703, 6709, 6719, 6733, 6751, 6773, 6799, 6829, 6863
6703, 6709, 6719, 6733	2n^2 + 6701	Complex	0+/-57.8835036949215i	423 Primes = 42.30%	6703, 6709, 6719, 6733, 6751, 6773, 6799, 6829, 6863, 6901
6983, 6991, 6997, 7001	-1n^2 + 11n + 6973	Real	-78.185422864439 +89.185422864439	395 Primes = 39.50%	6983, 6991, 6997, 7001, 7003, 7003, 7001, 6997, 6991, 6983	841, 361, -1369
7043, 7057, 7069, 7079	-1n^2 + 17n + 7027	Real	-75.75704718301 +92.75704718301	399 Primes = 39.90%	7043, 7057, 7069, 7079, 7087, 7093, 7097, 7099, 7099, 7097	6889, 2809, -6241
7211, 7213, 7219, 7229	2n^2 - 4n + 7213	Complex	1+/-60.045815840906i	490 Primes = 49.00%	7211, 7213, 7219, 7229, 7243, 7261, 7283, 7309, 7339, 7373
7219, 7229, 7237	-1n^2 + 13n + 7207	Real	-78.6425275640795 +91.6425275640795	408 Primes = 40.80%	7219, 7229, 7237, 7243, 7247, 7249, 7249, 7247, 7243, 7237	-1681
7219, 7229, 7237, 7243	-1n^2 + 11n + 7219	Real	-79.6425275640795 +90.6425275640795	407 Primes = 40.70%	7229, 7237, 7243, 7247, 7249, 7249, 7247, 7243, 7237, 7229	-1681
7673, 7681, 7687, 7691	-1n^2 + 11n + 7663	Real	-82.2111737465645 +93.2111737465645	431 Primes = 43.10%	7673, 7681, 7687, 7691, 7693, 7693, 7691, 7687, 7681, 7673	5041
7867, 7873, 7877, 7879	-1n^2 + 9n + 7859	Real	-84.2651395537685 +93.2651395537685	448 Primes = 44.80%	7867, 7873, 7877, 7879, 7879, 7877, 7873, 7867, 7859, 7849	5329
7919, 7927, 7933, 7937	-1n^2 + 11n + 7909	Real	-83.602469101591 +94.602469101591	369 Primes = 36.90%	7919, 7927, 7933, 7937, 7939, 7939, 7937, 7933, 7927, 7919	-516961
7963, 7993, 8009, 8011	-7n^2 + 51n + 7919	Real	-30.18843196129879 +37.47414624701307	358 Primes = 35.80%	7963, 7993, 8009, 8011, 7999, 7973, 7933, 7879, 7811, 7729	-466489, -546121
8017, 8039, 8053, 8059	-4n^2 + 34n + 7987	Real	-40.63666282984288 +49.13666282984288	291 Primes = 29.10%	8017, 8039, 8053, 8059, 8057, 8047, 8029, 8003, 7969, 7927	49
8167, 8171, 8179, 8191	2n^2 - 2n + 8167	Complex	0.5+/-63.90031298827875i	379 Primes = 37.90%	8167, 8171, 8179, 8191, 8207, 8227, 8251, 8279, 8311, 8347
8191, 8209, 8219, 8221	-4n^2 + 30n + 8165	Real	-41.58555447990025 +49.08555447990025	309 Primes = 30.90%	8191, 8209, 8219, 8221, 8215, 8201, 8179, 8149, 8111, 8065	6889, 6241
8231, 8233, 8237, 8243	n^2 - n + 8231	Complex	0.5+/-90.723480973781i	386 Primes = 38.60%	8231, 8233, 8237, 8243, 8251, 8261, 8273, 8287, 8303, 8321	17161, 44521, 564001
8363, 8369, 8377, 8387	n^2 + 3n + 8359	Complex	-1.5+/-91.4152613079455i	464 Primes = 46.40%	8363, 8369, 8377, 8387, 8399, 8413, 8429, 8447, 8467, 8489
8689, 8693, 8699, 8707	n^2 + n + 8687	Complex	-0.5+/-93.2027360113425i	229 Primes = 22.90%	8689, 8693, 8699, 8707, 8717, 8729, 8743, 8759, 8777, 8797
8821, 8831, 8837, 8839	-2n^2 + 16n + 8807	Real	-62.47932009279275 +70.47932009279275	411 Primes = 41.10%	8821, 8831, 8837, 8839, 8837, 8831, 8821, 8807, 8789, 8767	-961, -34969, -139129, -1329409
8933, 8941, 8951, 8963	n^2 + 5n + 8927	Complex	-2.5+/-94.449722074763i	415 Primes = 41.50%	8933, 8941, 8951, 8963, 8977, 8993, 9011, 9031, 9053, 9077	279841
9001, 9007, 9011, 9013	-1n^2 + 9n + 8993	Real	-90.43813775296 +99.43813775296	339 Primes = 33.90%	9001, 9007, 9011, 9013, 9013, 9011, 9007, 9001, 8993, 8983	-80089
9041, 9043, 9049, 9059	2n^2 - 4n + 9043	Complex	1+/-67.23466367879i	387 Primes = 38.70%	9041, 9043, 9049, 9059, 9073, 9091, 9113, 9139, 9169, 9203	10609, 38809, 177241, 1164241

* Polynomials derived from four consecutive primes.