
theorem
  7901 is prime
proof
  now
    7901 = 2*3950 + 1; hence not 2 divides 7901 by NAT_4:9;
    7901 = 3*2633 + 2; hence not 3 divides 7901 by NAT_4:9;
    7901 = 5*1580 + 1; hence not 5 divides 7901 by NAT_4:9;
    7901 = 7*1128 + 5; hence not 7 divides 7901 by NAT_4:9;
    7901 = 11*718 + 3; hence not 11 divides 7901 by NAT_4:9;
    7901 = 13*607 + 10; hence not 13 divides 7901 by NAT_4:9;
    7901 = 17*464 + 13; hence not 17 divides 7901 by NAT_4:9;
    7901 = 19*415 + 16; hence not 19 divides 7901 by NAT_4:9;
    7901 = 23*343 + 12; hence not 23 divides 7901 by NAT_4:9;
    7901 = 29*272 + 13; hence not 29 divides 7901 by NAT_4:9;
    7901 = 31*254 + 27; hence not 31 divides 7901 by NAT_4:9;
    7901 = 37*213 + 20; hence not 37 divides 7901 by NAT_4:9;
    7901 = 41*192 + 29; hence not 41 divides 7901 by NAT_4:9;
    7901 = 43*183 + 32; hence not 43 divides 7901 by NAT_4:9;
    7901 = 47*168 + 5; hence not 47 divides 7901 by NAT_4:9;
    7901 = 53*149 + 4; hence not 53 divides 7901 by NAT_4:9;
    7901 = 59*133 + 54; hence not 59 divides 7901 by NAT_4:9;
    7901 = 61*129 + 32; hence not 61 divides 7901 by NAT_4:9;
    7901 = 67*117 + 62; hence not 67 divides 7901 by NAT_4:9;
    7901 = 71*111 + 20; hence not 71 divides 7901 by NAT_4:9;
    7901 = 73*108 + 17; hence not 73 divides 7901 by NAT_4:9;
    7901 = 79*100 + 1; hence not 79 divides 7901 by NAT_4:9;
    7901 = 83*95 + 16; hence not 83 divides 7901 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7901 & n is prime
  holds not n divides 7901 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
