A348430 a(n) is the least prime of the form x+2 where x is the product of n consecutive primes.

3, 5, 17, 107, 215443, 15017, 1616617, 19657257924643, 8618654420263, 3234846617, 100280245067, 3710369067407, 19818939413097309267215847601753, 102481630431415237, 307444891294245707, 320460058359035439847, 961380175077106319537

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..222

Example

a(4) = 17*19*23*29+2 because that is prime while 2*3*5*7+2, 3*5*7*11+2, ..., 13*17*19*23+2 are not.

Maple

f:= proc(n) local P, i, r;
  P:= mul(ithprime(i), i=2..n+1);
  for i from 2 do
    r:= P+2;
    if isprime(r) then return r fi;
    P:= P/ithprime(i)*ithprime(i+n);
  od
end proc:
map(f, [$0..20]);

Mathematica

a[n_] := Module[{x = Product[Prime[i], {i, 2, n + 1}], p1 = 3, p2 = Prime[n + 2]}, While[! PrimeQ[x + 2], x *= (p2/p1); p1 = NextPrime[p1]; p2 = NextPrime[p2]]; x + 2]; Array[a, 17, 0] (* Amiram Eldar, Jan 25 2022 *)

Crossrefs

Cf. A347866, A083562.

Sequence in context: A084723 A288376 A096178 * A107312 A083213 A171271

Adjacent sequences: A348427 A348428 A348429 * A348431 A348432 A348433

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 25 2022

Status

approved