Sophie Germain: mathématicienne extraordinaire - Scripps College

Sophie Germain’s Theorems 62
Table 1.
Odd primes p up to 193 with q = 2kp + 1 prime for k ∈ {1, 2, 4, 5, 7, 8}
p k q=2kp+1 p k q=2kp+1 p k q=2kp+1
3* 1 7 59 7 827 131* 1 263
5* 1 11 61 8 977 137 4 1097
7 2 29 67 2 269 139 2 557
11* 1 23 71 4 569 149 4 1193
13 2 53 73 2 293 151 5 1511
17 4 137 79 2 317 157 5 1571
19 5 191 83* 1 167 163 2 653
23* 1 47 89* 1 179 167 7 2339
29* 1 59 97 2 389 173* 1 347
31 5 11 101 4 809 179* 1 359
37 2 149 103 5 1031 181 5 1811
41* 1 83 107 4 857 191* 1 383
43 2 173 109 5 1091 193 2 773
47 7 659 113* 1 227
53* 1 107 127 2 509 *Germain prime
5.2.1 Germain Primes
Are there infinitely many Sophie Germain primes Even today, many number
theorists ponder this question. Data are being compiled, books are being
written, and computer programs are running even as you read this,
searching for new and larger Germain primes. The largest known Sophie