p:=Array([7, 31, 127, 17, 73, 23, 89, 8191, 43, 151, 257, 131071, 524287, 41, 337, 683, 47, 178481, 241, 601, 1801, 2731, 262657, 113, 233, 1103, 2089, 331, 2147483647, 65537, 599479, 43691, 71, 122921, 109, 223, 616318177, 174763, 79, 121369, 61681]);
cnt:=0;
for k from 1 by 2 do
flag:=0;
for i from 1 to ArrayNumElems(p) do
for n from 1 to order(2, p[i]) do
if (3*5*11*13*19*29*37*k*2^n-1)mod p[i]=0 then
flag:=1;
break;
end if;
end do;
if flag=1 then break; end if;
end do;
if flag=0 then printf("k=%a is free\n", k); cnt:=cnt+1;end if;
if cnt=1 then break; end if;
end do;
Last updated 20 November 2002