A326228 Primes p such that m - p#/6 or p#/6 - n is not in A002822 (twin ranks), where m (resp. n) is the next larger (resp. smaller) twin rank w.r.t. p#/6, and # = A034386 (primorial).

41, 227, 307, 311, 349, 457, 613

Offset: 1

Author

M. F. Hasler, Jun 24 2019

Keywords

• nonn
• hard
• more

Comments

Related to the "Twin Fortune Conjecture" (A. Dinculescu) which states that the distance between p#/6 and the next larger or smaller n in A002822 (twin rank, such that 6n +- 1 are twin primes) is again a twin rank; very similar to Fortune's Conjecture, cf. A005235.

For a(1) = 41, the non twin rank is p#/6 - n, for all other terms listed here, it is m - p#/6. However, in these cases, the other distance is a twin rank. For all other primes, both distances are twin ranks.

Crossrefs

Cf. A002822 (twin ranks), A034386 (primorial), A005235 (Fortunate numbers).

Programs

PARI

is(p)={ my(m=A034386(p)/6,n=m); until(is_A002822(n-=1),); (is_A002822(m-n) || ((n=m) && !until(is_A002822(m+=1),) && is_A002822(m-n))) && isprime(p)}