
theorem
  7949 is prime
proof
  now
    7949 = 2*3974 + 1; hence not 2 divides 7949 by NAT_4:9;
    7949 = 3*2649 + 2; hence not 3 divides 7949 by NAT_4:9;
    7949 = 5*1589 + 4; hence not 5 divides 7949 by NAT_4:9;
    7949 = 7*1135 + 4; hence not 7 divides 7949 by NAT_4:9;
    7949 = 11*722 + 7; hence not 11 divides 7949 by NAT_4:9;
    7949 = 13*611 + 6; hence not 13 divides 7949 by NAT_4:9;
    7949 = 17*467 + 10; hence not 17 divides 7949 by NAT_4:9;
    7949 = 19*418 + 7; hence not 19 divides 7949 by NAT_4:9;
    7949 = 23*345 + 14; hence not 23 divides 7949 by NAT_4:9;
    7949 = 29*274 + 3; hence not 29 divides 7949 by NAT_4:9;
    7949 = 31*256 + 13; hence not 31 divides 7949 by NAT_4:9;
    7949 = 37*214 + 31; hence not 37 divides 7949 by NAT_4:9;
    7949 = 41*193 + 36; hence not 41 divides 7949 by NAT_4:9;
    7949 = 43*184 + 37; hence not 43 divides 7949 by NAT_4:9;
    7949 = 47*169 + 6; hence not 47 divides 7949 by NAT_4:9;
    7949 = 53*149 + 52; hence not 53 divides 7949 by NAT_4:9;
    7949 = 59*134 + 43; hence not 59 divides 7949 by NAT_4:9;
    7949 = 61*130 + 19; hence not 61 divides 7949 by NAT_4:9;
    7949 = 67*118 + 43; hence not 67 divides 7949 by NAT_4:9;
    7949 = 71*111 + 68; hence not 71 divides 7949 by NAT_4:9;
    7949 = 73*108 + 65; hence not 73 divides 7949 by NAT_4:9;
    7949 = 79*100 + 49; hence not 79 divides 7949 by NAT_4:9;
    7949 = 83*95 + 64; hence not 83 divides 7949 by NAT_4:9;
    7949 = 89*89 + 28; hence not 89 divides 7949 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7949 & n is prime
  holds not n divides 7949 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
