Thread: Superprime gaps
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Old 2018-12-30, 16:00   #3
CRGreathouse
 
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Aug 2006

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See also A073131.

Probably there are infinitely many gaps of length 6, but it seems hopeless to prove, even given a proof of the twin prime conjecture. The first few positions with such a gap:

Code:
2, 3, 17, 405, 695, 891, 1016, 1406, 1782, 1886, 1982, 2052, 2070, 2078, 2753, 3131, 3758, 3949, 4130, 4133, 4312, 4561, 4745, 4922, 5307, 5415, 5462, 5917, 6457, 6925, 7022, 7459, 7802, 8268, 8923, 9025, 9265, 9787, 9849, 10119, 10522, 10962, 11153, 11299, 11678, 11958, 11962, 12087, 12109, 12129, 12317, 12396, 12753, 13335, 13685, 13804, 14062, 15369, 16148, 16314, 16888, 16921, 17092, 17112, 17154, 17271, 18251, 19726, 20282, 20572, 20863, 21030, 22580, 22753, 23913, 24479, 25379, 25476, 25845, 28051, 28125, 29811, 30818, 32257, 32837, 32960, 33030, 33067, 33085, 33295, 33312, 34167, 34229, 34524, 34583, 34850, 35088, 35502, 35932, 36636, 36827, 37133, 37281, 37909, 37950, 38239, 38528, 38709, 38782, 39331, 39419, 40253, 40399, 40739, 41804, 42375, 43089, 43180, 43432, 44236, 44529, 44568, 44801, 44828, 44960, 45283, 45327, 45394, 45633, 45787, 46269, 46327, 46559, 47008, 47235, 47668, 48038, 48766, 49835, 49892, 50051, 51352, 51476, 52206, 52347, 52554, 52971, 53043, 53617, 54725, 54934, 55000, 55074, 55170, 56372, 56390, 56887, 56929, 58683, 58707, 58752, 58950, 60612, 61393, 65527, 66647, 66684, 67330, 67387, 67941, 68111, 68732, 68765, 69281, 69305, 69352, 70035, 71172, 71573, 73506, 73826, 74460, 75259, 75275, 76092
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