
theorem
  7951 is prime
proof
  now
    7951 = 2*3975 + 1; hence not 2 divides 7951 by NAT_4:9;
    7951 = 3*2650 + 1; hence not 3 divides 7951 by NAT_4:9;
    7951 = 5*1590 + 1; hence not 5 divides 7951 by NAT_4:9;
    7951 = 7*1135 + 6; hence not 7 divides 7951 by NAT_4:9;
    7951 = 11*722 + 9; hence not 11 divides 7951 by NAT_4:9;
    7951 = 13*611 + 8; hence not 13 divides 7951 by NAT_4:9;
    7951 = 17*467 + 12; hence not 17 divides 7951 by NAT_4:9;
    7951 = 19*418 + 9; hence not 19 divides 7951 by NAT_4:9;
    7951 = 23*345 + 16; hence not 23 divides 7951 by NAT_4:9;
    7951 = 29*274 + 5; hence not 29 divides 7951 by NAT_4:9;
    7951 = 31*256 + 15; hence not 31 divides 7951 by NAT_4:9;
    7951 = 37*214 + 33; hence not 37 divides 7951 by NAT_4:9;
    7951 = 41*193 + 38; hence not 41 divides 7951 by NAT_4:9;
    7951 = 43*184 + 39; hence not 43 divides 7951 by NAT_4:9;
    7951 = 47*169 + 8; hence not 47 divides 7951 by NAT_4:9;
    7951 = 53*150 + 1; hence not 53 divides 7951 by NAT_4:9;
    7951 = 59*134 + 45; hence not 59 divides 7951 by NAT_4:9;
    7951 = 61*130 + 21; hence not 61 divides 7951 by NAT_4:9;
    7951 = 67*118 + 45; hence not 67 divides 7951 by NAT_4:9;
    7951 = 71*111 + 70; hence not 71 divides 7951 by NAT_4:9;
    7951 = 73*108 + 67; hence not 73 divides 7951 by NAT_4:9;
    7951 = 79*100 + 51; hence not 79 divides 7951 by NAT_4:9;
    7951 = 83*95 + 66; hence not 83 divides 7951 by NAT_4:9;
    7951 = 89*89 + 30; hence not 89 divides 7951 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7951 & n is prime
  holds not n divides 7951 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
