
theorem
  1951 is prime
proof
  now
    1951 = 2*975 + 1; hence not 2 divides 1951 by NAT_4:9;
    1951 = 3*650 + 1; hence not 3 divides 1951 by NAT_4:9;
    1951 = 5*390 + 1; hence not 5 divides 1951 by NAT_4:9;
    1951 = 7*278 + 5; hence not 7 divides 1951 by NAT_4:9;
    1951 = 11*177 + 4; hence not 11 divides 1951 by NAT_4:9;
    1951 = 13*150 + 1; hence not 13 divides 1951 by NAT_4:9;
    1951 = 17*114 + 13; hence not 17 divides 1951 by NAT_4:9;
    1951 = 19*102 + 13; hence not 19 divides 1951 by NAT_4:9;
    1951 = 23*84 + 19; hence not 23 divides 1951 by NAT_4:9;
    1951 = 29*67 + 8; hence not 29 divides 1951 by NAT_4:9;
    1951 = 31*62 + 29; hence not 31 divides 1951 by NAT_4:9;
    1951 = 37*52 + 27; hence not 37 divides 1951 by NAT_4:9;
    1951 = 41*47 + 24; hence not 41 divides 1951 by NAT_4:9;
    1951 = 43*45 + 16; hence not 43 divides 1951 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1951 & n is prime
  holds not n divides 1951 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
