There are endlessly many identities of the form pFp-1[rational] = pile of Gammas(rationals), but, as Dick Askey pointed out to me decades ago, the rationals all seem to be made out of primes < 7. I've always known how to construct one with 7s, but the hardware (and my stomach) were never up to it. Just to get it over with, Sum[(((j^13 + ((946722645184512*j^12 + 3397234214391808*j^11 + 7324312847932416*j^10 + 10575837135607296*j^9 + 10789977229862400*j^8 + 7994097957085696*j^7 + 4349780625735744*j^6 + 1736115415231328*j^5 + 501325200097728*j^4 + 101649833417016*j^3 + 13682157776100*j^2 + 1093720984200*j + 39131717625)/ 119811560185856))*(-1)^j*((j - 1/2)!)^2*(6*j + 1/2)!*(7*j + 1/2)!)/((j + 1)!* (7*j + 6)!*(7*j + 7)!)), {j, 0, Infinity}] == Pi/14625434593 This is thirteen or so 16F15[-6^6/7^7]s. The XP Macsyma (compiled for a 286 in NT) that disgorged this was so effete that afterward, it claimed 2F1[1/2,1/2;2] = 0, and when asked for the pFp-1s for the above, said Error: FACTOR ran out of primes. --rwg