
theorem
  3797 is prime
proof
  now
    3797 = 2*1898 + 1; hence not 2 divides 3797 by NAT_4:9;
    3797 = 3*1265 + 2; hence not 3 divides 3797 by NAT_4:9;
    3797 = 5*759 + 2; hence not 5 divides 3797 by NAT_4:9;
    3797 = 7*542 + 3; hence not 7 divides 3797 by NAT_4:9;
    3797 = 11*345 + 2; hence not 11 divides 3797 by NAT_4:9;
    3797 = 13*292 + 1; hence not 13 divides 3797 by NAT_4:9;
    3797 = 17*223 + 6; hence not 17 divides 3797 by NAT_4:9;
    3797 = 19*199 + 16; hence not 19 divides 3797 by NAT_4:9;
    3797 = 23*165 + 2; hence not 23 divides 3797 by NAT_4:9;
    3797 = 29*130 + 27; hence not 29 divides 3797 by NAT_4:9;
    3797 = 31*122 + 15; hence not 31 divides 3797 by NAT_4:9;
    3797 = 37*102 + 23; hence not 37 divides 3797 by NAT_4:9;
    3797 = 41*92 + 25; hence not 41 divides 3797 by NAT_4:9;
    3797 = 43*88 + 13; hence not 43 divides 3797 by NAT_4:9;
    3797 = 47*80 + 37; hence not 47 divides 3797 by NAT_4:9;
    3797 = 53*71 + 34; hence not 53 divides 3797 by NAT_4:9;
    3797 = 59*64 + 21; hence not 59 divides 3797 by NAT_4:9;
    3797 = 61*62 + 15; hence not 61 divides 3797 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3797 & n is prime
  holds not n divides 3797 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
