A127344 Product of 12 consecutive primes.

7420738134810, 152125131763605, 2180460221945005, 20496326086283047, 155186468939000213, 832363787945546597, 3905707004975257109, 15393080549020130959, 57521511525285752531, 182568275710689562381, 497341164867050876831, 1331590860773071702483

Offset: 1

Author

Artur Jasinski, Jan 11 2007

Keywords

• nonn

Comments

a(n) = coefficient of x^0 of the polynomial Prod_{j=0,11}(x-prime(n+j)) of degree 12; the roots of this polynomial are prime(n), ..., prime(n+11).

Crossrefs

Cf. A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, A127342, A127343.

Programs

Magma

[&*[ NthPrime(n+k): k in [0..11] ]: n in [1..50] ]; // Vincenzo Librandi, Apr 03 2011

Maple

A127344 := proc(n) mul(ithprime(n+k),k=0..11) ; end proc: # R. J. Mathar, Apr 05 2011

Mathematica

a = {}; Do[AppendTo[a, Product[Prime[x + n], {n, 0, 11}]], {x, 1, 50}]; a
Times@@@Partition[Prime[Range[50]],12,1] (* Harvey P. Dale, Oct 21 2011 *)

PARI

{m=10;k=12;for(n=0,m-1,print1(a=prod(j=1,k,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 21 2007

PARI

{m=10;k=12;for(n=1,m,print1(polcoeff(prod(j=0,k-1,(x-prime(n+j))),0),","))} \\ Klaus Brockhaus, Jan 21 2007

Extensions

Edited by Klaus Brockhaus, Jan 21 2007