
theorem
  1901 is prime
proof
  now
    1901 = 2*950 + 1; hence not 2 divides 1901 by NAT_4:9;
    1901 = 3*633 + 2; hence not 3 divides 1901 by NAT_4:9;
    1901 = 5*380 + 1; hence not 5 divides 1901 by NAT_4:9;
    1901 = 7*271 + 4; hence not 7 divides 1901 by NAT_4:9;
    1901 = 11*172 + 9; hence not 11 divides 1901 by NAT_4:9;
    1901 = 13*146 + 3; hence not 13 divides 1901 by NAT_4:9;
    1901 = 17*111 + 14; hence not 17 divides 1901 by NAT_4:9;
    1901 = 19*100 + 1; hence not 19 divides 1901 by NAT_4:9;
    1901 = 23*82 + 15; hence not 23 divides 1901 by NAT_4:9;
    1901 = 29*65 + 16; hence not 29 divides 1901 by NAT_4:9;
    1901 = 31*61 + 10; hence not 31 divides 1901 by NAT_4:9;
    1901 = 37*51 + 14; hence not 37 divides 1901 by NAT_4:9;
    1901 = 41*46 + 15; hence not 41 divides 1901 by NAT_4:9;
    1901 = 43*44 + 9; hence not 43 divides 1901 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1901 & n is prime
  holds not n divides 1901 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
