
theorem
  1949 is prime
proof
  now
    1949 = 2*974 + 1; hence not 2 divides 1949 by NAT_4:9;
    1949 = 3*649 + 2; hence not 3 divides 1949 by NAT_4:9;
    1949 = 5*389 + 4; hence not 5 divides 1949 by NAT_4:9;
    1949 = 7*278 + 3; hence not 7 divides 1949 by NAT_4:9;
    1949 = 11*177 + 2; hence not 11 divides 1949 by NAT_4:9;
    1949 = 13*149 + 12; hence not 13 divides 1949 by NAT_4:9;
    1949 = 17*114 + 11; hence not 17 divides 1949 by NAT_4:9;
    1949 = 19*102 + 11; hence not 19 divides 1949 by NAT_4:9;
    1949 = 23*84 + 17; hence not 23 divides 1949 by NAT_4:9;
    1949 = 29*67 + 6; hence not 29 divides 1949 by NAT_4:9;
    1949 = 31*62 + 27; hence not 31 divides 1949 by NAT_4:9;
    1949 = 37*52 + 25; hence not 37 divides 1949 by NAT_4:9;
    1949 = 41*47 + 22; hence not 41 divides 1949 by NAT_4:9;
    1949 = 43*45 + 14; hence not 43 divides 1949 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1949 & n is prime
  holds not n divides 1949 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
