A058233 Primes p such that p#+1 is divisible by the next prime after p.

2, 17, 1459, 2999

Offset: 1

Author

Carlos Rivera, Dec 01 2000

Keywords

• nice
• nonn
• more

Comments

No additional terms through the 100000th prime. - Harvey P. Dale, Mar 12 2014

a(5) > prime(1400000) = 22182343. - Robert Price, Apr 02 2018

Examples

			2*3*5*7*11*13*17+1 is divisible by 19.
		

Links

• Carlos Rivera, Puzzle 117: Certain p#+1 values, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A006862, A066735, A341804.

Programs

Mathematica

primorial[n_] := Product[ Prime[k], {k, 1, PrimePi[n]}]; Select[ Prime[ Range[1000]], Divisible[ primorial[#] + 1, NextPrime[#]] &] (* Jean-François Alcover, Aug 19 2013 *)
Module[{prs=Prime[Range[500]]},Transpose[Select[Thread[{Rest[ FoldList[ Times, 1,prs]], prs}], Divisible[ First[#]+1, NextPrime[Last[#]]]&]][[2]]] (* Harvey P. Dale, Mar 12 2014 *)

Python

from sympy import nextprime
A058233_list, p, q, r = [], 2, 3, 2
for _ in range(10**3):
    if (r+1) % q == 0:
        A058233_list.append(p)
    r *= q
    p, q = q, nextprime(q) # Chai Wah Wu, Sep 27 2021