
theorem
  2903 is prime
proof
  now
    2903 = 2*1451 + 1; hence not 2 divides 2903 by NAT_4:9;
    2903 = 3*967 + 2; hence not 3 divides 2903 by NAT_4:9;
    2903 = 5*580 + 3; hence not 5 divides 2903 by NAT_4:9;
    2903 = 7*414 + 5; hence not 7 divides 2903 by NAT_4:9;
    2903 = 11*263 + 10; hence not 11 divides 2903 by NAT_4:9;
    2903 = 13*223 + 4; hence not 13 divides 2903 by NAT_4:9;
    2903 = 17*170 + 13; hence not 17 divides 2903 by NAT_4:9;
    2903 = 19*152 + 15; hence not 19 divides 2903 by NAT_4:9;
    2903 = 23*126 + 5; hence not 23 divides 2903 by NAT_4:9;
    2903 = 29*100 + 3; hence not 29 divides 2903 by NAT_4:9;
    2903 = 31*93 + 20; hence not 31 divides 2903 by NAT_4:9;
    2903 = 37*78 + 17; hence not 37 divides 2903 by NAT_4:9;
    2903 = 41*70 + 33; hence not 41 divides 2903 by NAT_4:9;
    2903 = 43*67 + 22; hence not 43 divides 2903 by NAT_4:9;
    2903 = 47*61 + 36; hence not 47 divides 2903 by NAT_4:9;
    2903 = 53*54 + 41; hence not 53 divides 2903 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2903 & n is prime
  holds not n divides 2903 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
