A256072 Primes that cannot be represented as x*y + x + y, where x >= y > 1.

2, 3, 5, 7, 13, 37, 61, 73, 157, 193, 277, 313, 397, 421, 457, 541, 613, 661, 673, 733, 757, 877, 997, 1093, 1153, 1201, 1213, 1237, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1933, 1993, 2017, 2137, 2341, 2473, 2557, 2593, 2797, 2857, 2917, 3061, 3217, 3253, 3313

Offset: 1

Author

Alex Ratushnyak, Mar 14 2015

Keywords

• nonn

Comments

Primes in A254636.

Crossrefs

Cf. A000040, A254636, A005383, A079147.

Programs

PARI

v=[];for(m=2,500,for(k=m,500,if(isprime(P=k*m+k+m),v=concat(v,P))));v=vecsort(v,,8);forprime(p=1,2000,if(!vecsearch(v,p),print1(p,", "))) \\ Derek Orr, Mar 21 2015

Python

import sympy
from sympy import isprime
TOP = 10000
a = [0]*TOP
for y in range(2, TOP//2):
  for x in range(y, TOP//2):
    k = x*y + x + y
    if k>=TOP: break
    a[k]+=1
print([n for n in range(TOP) if a[n]==0 and isprime(n)])

Formula

{2, 7} UNION A005383 = {7} UNION A079147. - Chai Wah Wu, Oct 15 2024