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Sophie Germain primes
A prime p such that 2p + 1 is also prime. more

The first 600 Sophie Germain primes :
2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1439, 1451, 1481, 1499, 1511, 1559, 1583, 1601, 1733, 1811, 1889, 1901, 1931, 1973, 2003, 2039, 2063, 2069, 2129, 2141, 2273, 2339, 2351, 2393, 2399, 2459, 2543, 2549, 2693, 2699, 2741, 2753, 2819, 2903, 2939, 2963, 2969, 3023, 3299, 3329, 3359, 3389, 3413, 3449, 3491, 3539, 3593, 3623, 3761, 3779, 3803, 3821, 3851, 3863, 3911, 4019, 4073, 4211, 4271, 4349, 4373, 4391, 4409, 4481, 4733, 4793, 4871, 4919, 4943, 5003, 5039, 5051, 5081, 5171, 5231, 5279, 5303, 5333, 5399, 5441, 5501, 5639, 5711, 5741, 5849, 5903, 6053, 6101, 6113, 6131, 6173, 6263, 6269, 6323, 6329, 6449, 6491, 6521, 6551, 6563, 6581, 6761, 6899, 6983, 7043, 7079, 7103, 7121, 7151, 7193, 7211, 7349, 7433, 7541, 7643, 7649, 7691, 7823, 7841, 7883, 7901, 8069, 8093, 8111, 8243, 8273, 8513, 8663, 8693, 8741, 8951, 8969, 9029, 9059, 9221, 9293, 9371, 9419, 9473, 9479, 9539, 9629, 9689, 9791, 10061, 10091, 10163, 10253, 10271, 10313, 10331, 10529, 10589, 10613, 10691, 10709, 10733, 10781, 10799, 10883, 11171, 11321, 11369, 11393, 11471, 11519, 11549, 11579, 11699, 11783, 11801, 11813, 11831, 11909, 11939, 12011, 12041, 12101, 12119, 12203, 12263, 12329, 12653, 12671, 12791, 12821, 12899, 12923, 12959, 13001, 13049, 13229, 13313, 13451, 13463, 13553, 13619, 13649, 13763, 13883, 13901, 13913, 14009, 14081, 14153, 14159, 14249, 14303, 14321, 14489, 14561, 14621, 14669, 14699, 14741, 14783, 14831, 14879, 14939, 15101, 15161, 15173, 15233, 15269, 15401, 15569, 15629, 15773, 15791, 15803, 15923, 16001, 16091, 16253, 16301, 16421, 16493, 16553, 16673, 16811, 16823, 16883, 16931, 17159, 17183, 17291, 17333, 17351, 17579, 17669, 17681, 17939, 17981, 18041, 18131, 18149, 18191, 18233, 18341, 18443, 18461, 18731, 18773, 18803, 18899, 19163, 19301, 19319, 19373, 19391, 19433, 19553, 19559, 19661, 19709, 19751, 19889, 19913, 19919, 19991, 20063, 20249, 20369, 20393, 20411, 20441, 20693, 20753, 20759, 20771, 20789, 20879, 20921, 20939, 20963, 21011, 21089, 21149, 21179, 21221, 21341, 21383, 21419, 21611, 21701, 21713, 21803, 21893, 22013, 22079, 22133, 22259, 22271, 22343, 22349, 22409, 22433, 22469, 22481, 22541, 22751, 22853, 22943, 23099, 23279, 23321, 23339, 23459, 23561, 23603, 23669, 23753, 23819, 23909, 23981, 24203, 24239, 24281, 24473, 24509, 24551, 24611, 24683, 24749, 24971, 25073, 25229, 25523, 25601, 25643, 25673, 25703, 25799, 25841, 25913, 25919, 26111, 26189, 26459, 26501, 26573, 26633, 26849, 26879, 26891, 26993, 27143, 27281, 27479, 27539, 27551, 27581, 27743, 27773, 27809, 27893, 27983, 28001, 28019, 28403, 28499, 28559, 28571, 28643, 28751, 28793, 28859, 28901, 28949, 28961, 29021, 29033, 29201, 29339, 29363, 29453, 29483, 29531, 29723, 29873, 30269, 30323, 30389, 30449, 30671, 30689, 30773, 30851, 30983, 31019, 31151, 31253, 31319, 31469, 31649, 31721, 31793, 31799, 31859, 32003, 32009, 32141, 32159, 32381, 32531, 32561, 32573, 32633, 32771, 32789, 32843, 32933, 33023, 33053, 33119, 33179, 33191, 33461, 33479, 33521, 33569, 33623, 33713, 33749, 33773, 33809, 33941, 34253, 34283, 34319, 34439, 34631, 34883, 34913, 34949, 35069, 35081, 35099, 35111, 35291, 35573, 35831, 35933, 35993, 35999, 36083, 36191, 36251, 36353, 36383, 36479, 36563, 36629, 36761, 36791, 36821, 36923, 36929, 37013, 37049, 37139, 37181, 37253, 37379, 37619, 37853, 37871, 37991, 38039, 38183, 38189, 38201, 38231, 38303, 38333, 38453, 38459, 38501, 38639, 38669, 38723, 38861, 38873, 38891, 38933, 39089, 39233, 39239, 39419, 39443, 39521, 39551, 39569, 39659, 39779, 39953, 39971, 39983, 39989, 40193, 40283, 40343, 40559, 40763, 40823, 40853, 40949, 41081, 41231, 41243, 41381, 41399, 41603, 41609, 41621, 41669, 41729, 41969, 42023, 42071, 42089, 42131, 42221, 42359, 42473, 42611, 42719, 42743, 42821, 42923, 43013, 43313, 43391, 43541.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 26569516 values, from 2 to 10000000343).

n\r 0  1 
2126569515 2 
31026569515 3 
4013283194113286321 4 
518856045188588028854667 5 
60011026569514 6 
70531244253148981531633753114555314383 7 
806643473166417540663972106644567 8 
9008855992108855532008857991 9 
100885604518858802010008854667 10 
1112952313295361429525182951887129510442952376295223929522842951239

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.