> for p from 1 to 200000 do
> n:=6*p+1;
> br__a:=0;
> br__d:=0;
> for a from 1 to n do
> if(br__a=1) then br__a:=0; break; end if:
> g:=(a*n)^2;
> for d in divisors(g) do
> if(br__d=1) then br__d:=0; break; end if:
> v:=irem(a*n+d,4*a-1);
> if(v=0) then
> if(isprime(n) and (a>50)) then print(n,a,d,_prime_); end if:
> if(not isprime(n) and (a>6)) then print(n,a,d,ifactor(n)); end if:
> br__a:=1;
> br__d:=1;
> end if:
> end do:
> end do:
> end do:

                       22621, 105, 525, _prime_


                                             2
                       44521, 11, 211,  (211)


                     69841, 8, 16,  (211)  (331)


                       106591, 60, 180, _prime_


                                              2
                      109561, 10, 1655,  (331)


                       135151, 96, 12, _prime_


                       145861, 70, 14, _prime_


                        162451, 84, 6, _prime_


                    165169, 10, 662,  (331)  (499)


                       167521, 65, 13, _prime_


                        185959, 54, 4, _prime_


                       192949, 54, 729, _prime_


                       206299, 174, 29, _prime_


                    209101, 8, 1688,  (211)  (991)


                   221761, 10, 4220,  (211)  (1051)


                       225289, 70, 245, _prime_


                                              2
                       249001, 10, 998,  (499)


                       284551, 54, 81, _prime_


                   291391, 8, 89042,  (211)  (1381)


                                               2
                      292681, 10, 27050,  (541)


                       296221, 78, 507, _prime_


                    328021, 8, 2648,  (331)  (991)


                       329401, 51, 17, _prime_


                       333631, 78, 18, _prime_


                        361321, 72, 3, _prime_


                       375631, 120, 96, _prime_


                       378151, 84, 16, _prime_


                       395509, 55, 275, _prime_


                     399799, 8, 2,  (541)  (739)


                       400339, 56, 98, _prime_


                       409081, 55, 605, _prime_


                       426871, 102, 18, _prime_


                    457111, 10, 2,  (331)  (1381)


                       469351, 56, 16, _prime_


                        499711, 56, 8, _prime_


                       509581, 96, 48, _prime_


                   512719, 8, 2648,  (331)  (1549)


                    536131, 8, 4328,  (541)  (991)


                                               2
                      546121, 10, 14780,  (739)


                       557671, 76, 38, _prime_


                       568471, 81, 729, _prime_


                  568591, 10, 10820,  (541)  (1051)


                        571099, 56, 1, _prime_


                       594211, 75, 125, _prime_


                        639391, 52, 8, _prime_


                      689131, 147, 1029, _prime_


                       714151, 51, 153, _prime_


                        723451, 54, 6, _prime_


                    732349, 8, 5912,  (739)  (991)


                  747121, 8, 2341448,  (541)  (1381)


                      756571, 98, 1372, _prime_


                       757579, 51, 867, _prime_


                   772951, 8, 3992,  (499)  (1549)


                     776689, 8, 4,  (739)  (1051)


                        782461, 96, 2, _prime_


                       786031, 54, 486, _prime_


                        790519, 54, 9, _prime_


                        814501, 78, 2, _prime_


                    820579, 10, 5,  (211)  (3889)


                        833281, 57, 9, _prime_


                       836749, 51, 867, _prime_


                       894391, 54, 486, _prime_


                       909451, 60, 225, _prime_


                        915961, 76, 2, _prime_


                       931309, 72, 432, _prime_


                       954409, 84, 504, _prime_


                       978181, 66, 242, _prime_


                                              2
                       982081, 8, 7928,  (991)


                      996361, 60, 1800, _prime_


                     1003909, 105, 1575, _prime_


                   1013191, 8, 662,  (331)  (3061)


                    1019341, 8, 8,  (211)  (4831)


                  1020559, 10, 27620,  (739)  (1381)


                       1030759, 60, 12, _prime_


                      1035301, 85, 425, _prime_


                      1038811, 60, 150, _prime_


                      1053061, 54, 486, _prime_


                  1078729, 10, 16295,  (331)  (3259)


                      1083289, 60, 144, _prime_


                                                2
                     1104601, 10, 21020,  (1051)


                       1130431, 63, 81, _prime_


                     1138141, 130, 3380, _prime_


                       1151599, 56, 49, _prime_


                      1164199, 55, 275, _prime_


                       1190011, 52, 8, _prime_


                      1197751, 63, 1323, _prime_

>