A386540 Primes p such that 2p - 1, 3p - 2, (p + 1)/2, and (p + 2)/3 are also prime.
37, 2557, 3061, 5581, 88741, 124021, 157081, 178537, 216217, 216757, 217057, 330661, 344821, 352081, 387577, 423481, 459397, 477577, 521137, 790861, 806521, 865957, 869521, 1369657, 1517881, 1673401, 1704397, 1710661, 1970257, 2132797, 2292781, 2361781, 2680141
Offset: 1
Examples
37 is a term, since it is prime and 2*37 - 1 = 73, 3*37 - 2 = 109, (37 + 1)/2 = 19 and (37 + 2)/3 = 13 are all prime.
Links
- Robert Israel, Table of n, a(n) for n = 1..1000
Programs
-
Maple
select(p -> andmap(isprime,[p, 2*p-1,3*p-2,(p+1)/2,(p+2)/3]), [seq(1+12*i,i=1..10^6)]); # Robert Israel, Jul 25 2025
-
Mathematica
Select[Prime[Range[2*10^5]],AllTrue[{2#-1,3#-2,(#+1)/2,(#+2)/3},PrimeQ]&] (* James C. McMahon, Jul 25 2025 *) -
Python
from gmpy2 import is_prime def ok(p): return p&1 and p%3 == 1 and all(is_prime(q) for q in [p, 2*p-1, 3*p-2, (p+1)//2, (p+2)//3]) print([k for k in range(1, 10**7, 12) if ok(k)]) # Michael S. Branicky, Jul 25 2025
Comments