The Sequence database has more information: A057732 2^N+3 prime 1, 2, 3, 4, 6, 7, 12, 15, 16, 18, 28, 30, 55, 67, 84, 228, 390, 784, 1110, 1704, 2008, 2139, 2191, 2367, 2370, 4002, 4060, 4062, 4552, 5547, 8739, 17187, 17220, 17934, 20724, 22732, 25927, 31854, 33028, 35754, 38244, 39796, 40347, 55456, 58312, 122550 A050414 2^N-3 prime 3, 4, 5, 6, 9, 10, 12, 14, 20, 22, 24, 29, 94, 116, 122, 150, 174, 213, 221, 233, 266, 336, 452, 545, 689, 694, 850, 1736, 2321, 3237, 3954, 5630, 6756, 8770, 10572, 14114, 14400, 16460, 16680 2^N-3 is still leading the race at 17000, but the ratio has dropped quite a bit from 1.5. The bunchiness winner is with 2^N+3: N = both 4060 and 4062 give (probable) primes. Technical note: I've been using "probable prime" tests, and the notes in the sequence database mention this too. Rich -----Original Message----- From: Schroeppel, Richard Sent: Sat 10/7/2006 9:37 PM To: math-fun@mailman.xmission.com Cc: Schroeppel, Richard; rcs@cs.arizona.edu Subject: Primes in 2^N +-3 A curiosity: There seem to be 1.5 times as many primes of the form 2^N-3 as there are of the form 2^N+3. 2^N+3 is prime for N = 1 2 3 4 6 7 12 15 16 18 28 30 55 67 84 228 390 784 while 2^N-3 is prime for N = 3 4 5 6 9 10 12 14 20 22 24 29 94 116 122 150 174 213 221 233 266 336 452 545 689 694 850 (up to N=1000). The former sequence is divisible by 7 when N = 2 mod 3, while the latter is never a multiple of 7. Small primes other than 7 seem to strike both sequences equally. The large gaps (390-784, and 29-94) and general bunchiness (213, 221, 233; 689, 694) makes it hard to draw any firm conclusions. Rich