
theorem
  7963 is prime
proof
  now
    7963 = 2*3981 + 1; hence not 2 divides 7963 by NAT_4:9;
    7963 = 3*2654 + 1; hence not 3 divides 7963 by NAT_4:9;
    7963 = 5*1592 + 3; hence not 5 divides 7963 by NAT_4:9;
    7963 = 7*1137 + 4; hence not 7 divides 7963 by NAT_4:9;
    7963 = 11*723 + 10; hence not 11 divides 7963 by NAT_4:9;
    7963 = 13*612 + 7; hence not 13 divides 7963 by NAT_4:9;
    7963 = 17*468 + 7; hence not 17 divides 7963 by NAT_4:9;
    7963 = 19*419 + 2; hence not 19 divides 7963 by NAT_4:9;
    7963 = 23*346 + 5; hence not 23 divides 7963 by NAT_4:9;
    7963 = 29*274 + 17; hence not 29 divides 7963 by NAT_4:9;
    7963 = 31*256 + 27; hence not 31 divides 7963 by NAT_4:9;
    7963 = 37*215 + 8; hence not 37 divides 7963 by NAT_4:9;
    7963 = 41*194 + 9; hence not 41 divides 7963 by NAT_4:9;
    7963 = 43*185 + 8; hence not 43 divides 7963 by NAT_4:9;
    7963 = 47*169 + 20; hence not 47 divides 7963 by NAT_4:9;
    7963 = 53*150 + 13; hence not 53 divides 7963 by NAT_4:9;
    7963 = 59*134 + 57; hence not 59 divides 7963 by NAT_4:9;
    7963 = 61*130 + 33; hence not 61 divides 7963 by NAT_4:9;
    7963 = 67*118 + 57; hence not 67 divides 7963 by NAT_4:9;
    7963 = 71*112 + 11; hence not 71 divides 7963 by NAT_4:9;
    7963 = 73*109 + 6; hence not 73 divides 7963 by NAT_4:9;
    7963 = 79*100 + 63; hence not 79 divides 7963 by NAT_4:9;
    7963 = 83*95 + 78; hence not 83 divides 7963 by NAT_4:9;
    7963 = 89*89 + 42; hence not 89 divides 7963 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7963 & n is prime
  holds not n divides 7963 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
