
theorem
  1913 is prime
proof
  now
    1913 = 2*956 + 1; hence not 2 divides 1913 by NAT_4:9;
    1913 = 3*637 + 2; hence not 3 divides 1913 by NAT_4:9;
    1913 = 5*382 + 3; hence not 5 divides 1913 by NAT_4:9;
    1913 = 7*273 + 2; hence not 7 divides 1913 by NAT_4:9;
    1913 = 11*173 + 10; hence not 11 divides 1913 by NAT_4:9;
    1913 = 13*147 + 2; hence not 13 divides 1913 by NAT_4:9;
    1913 = 17*112 + 9; hence not 17 divides 1913 by NAT_4:9;
    1913 = 19*100 + 13; hence not 19 divides 1913 by NAT_4:9;
    1913 = 23*83 + 4; hence not 23 divides 1913 by NAT_4:9;
    1913 = 29*65 + 28; hence not 29 divides 1913 by NAT_4:9;
    1913 = 31*61 + 22; hence not 31 divides 1913 by NAT_4:9;
    1913 = 37*51 + 26; hence not 37 divides 1913 by NAT_4:9;
    1913 = 41*46 + 27; hence not 41 divides 1913 by NAT_4:9;
    1913 = 43*44 + 21; hence not 43 divides 1913 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1913 & n is prime
  holds not n divides 1913 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
