Twin Prime Calculator
Find twin primes (p, p+2), cousin primes (p, p+4), sexy primes (p, p+6), and prime constellations.
Range Settings
Definitions:
- Twin primes: (p, p+2) - differ by 2
- Cousin primes: (p, p+4) - differ by 4
- Sexy primes: (p, p+6) - differ by 6
Twin Primes
35
Cousin Primes
41
Sexy Primes
74
Total Primes
168
Largest Twin Pair Found
(881, 883)
Twin Prime Pairs (first 100)
(3, 5)(5, 7)(11, 13)(17, 19)(29, 31)(41, 43)(59, 61)(71, 73)(101, 103)(107, 109)(137, 139)(149, 151)(179, 181)(191, 193)(197, 199)(227, 229)(239, 241)(269, 271)(281, 283)(311, 313)(347, 349)(419, 421)(431, 433)(461, 463)(521, 523)(569, 571)(599, 601)(617, 619)(641, 643)(659, 661)(809, 811)(821, 823)(827, 829)(857, 859)(881, 883)
Prime Triplets (30 found)
(5, 7, 11)
(7, 11, 13)
(11, 13, 17)
(13, 17, 19)
(17, 19, 23)
(37, 41, 43)
(41, 43, 47)
(67, 71, 73)
(97, 101, 103)
(101, 103, 107)
(103, 107, 109)
(107, 109, 113)
(191, 193, 197)
(193, 197, 199)
(223, 227, 229)
(227, 229, 233)
(277, 281, 283)
(307, 311, 313)
(311, 313, 317)
(347, 349, 353)
Twin Prime Density
20.83%
Brun's Constant (partial)
1.518032
About Twin Primes
Twin Prime Conjecture
There are infinitely many twin primes. This conjecture remains unproven, though Yitang Zhang proved in 2013 that there are infinitely many prime pairs within 70 million of each other.
First Twin Primes
(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), ...