A127342 Product of 10 consecutive primes.

6469693230, 100280245065, 1236789689135, 10141675450907, 62298863484143, 266186053068611, 1085220062510491, 3766351981654057, 12091972151626183, 35224440615606707, 86239147714071593, 203079283326684719

Offset: 1

Author

Artur Jasinski, Jan 11 2007

Keywords

• nonn

Comments

a(n) = coefficient of x^0 of the polynomial Product_{j=0..9} (x-prime(n+j)) of degree 10; the roots of this polynomial are prime(n), ..., prime(n+9).

Crossrefs

Cf. A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, A127343, A127344.

Programs

Magma

[&*[ NthPrime(n+k): k in [0..9] ]: n in [1..50] ]; // Vincenzo Librandi, Apr 03 2011

Mathematica

a = {}; Do[AppendTo[a, Product[Prime[x + n], {n, 0, 9}]], {x, 1, 50}]; a
Times@@@Partition[Prime[Range[50]],10,1] (* Harvey P. Dale, Oct 21 2011 *)

PARI

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

PARI

{m=12;k=10;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