A051902 Minimal primorial safe primes: p and primorial*p + 1 are both primes.

5, 13, 61, 421, 4621, 150151, 8678671, 106696591, 2454021571, 71166625531, 401120980261, 170676977100631, 2129751844690471, 562558737261811291, 11682905869181336791, 97767475431570134191, 9613801750771063195351, 234576762718813941966541, 55008250857561869391153631

Offset

1,1

Comments

In A051888, 13 of the first 25 values are distinct, while here all corresponding min-primorial-safe-primes are different: {2,5,17,11,23,43,19,3,7,61,53,41,47}.

Links

Amiram Eldar, Table of n, a(n) for n = 1..349

Formula

a(n) = 1 + A002110(n)*A051887(n).

Example

The first five terms of A051887 are 2, so the first 5 terms have the form 1 + 2*A002110(n): 5, 13, 61, 421, 4621, which are smallest terms in A005385, A051644, A051646, A051648, A051649. The 6th term here is A051651(1) = A051887(6)*A002110(6) + 1 = 5*30030 + 1.

Mathematica

a[n_] := Module[{p = 2, r =Times @@ Prime[Range[n]]}, While[!PrimeQ[p * r + 1], p = NextPrime[p]]; p * r + 1]; Array[a, 20] (* Amiram Eldar, Feb 25 2025 *)

Prog

(PARI) a(n) = {my(p = 2, r = vecprod(primes(n))); while(!isprime(p * r + 1), p = nextprime(p+1)); p * r + 1; } \\ Amiram Eldar, Feb 25 2025

Crossrefs

Cf. A005385, A002110, A051644, A051646, A051648, A051649.

Sequence in context: A149568 A201805 A144725 * A269514 A149569 A149570

Adjacent sequences: A051899 A051900 A051901 * A051903 A051904 A051905

Keyword

nonn,changed

Author

Labos Elemer, Dec 16 1999

Status

approved