
theorem
  1051 is prime
proof
  now
    1051 = 2*525 + 1; hence not 2 divides 1051 by NAT_4:9;
    1051 = 3*350 + 1; hence not 3 divides 1051 by NAT_4:9;
    1051 = 5*210 + 1; hence not 5 divides 1051 by NAT_4:9;
    1051 = 7*150 + 1; hence not 7 divides 1051 by NAT_4:9;
    1051 = 11*95 + 6; hence not 11 divides 1051 by NAT_4:9;
    1051 = 13*80 + 11; hence not 13 divides 1051 by NAT_4:9;
    1051 = 17*61 + 14; hence not 17 divides 1051 by NAT_4:9;
    1051 = 19*55 + 6; hence not 19 divides 1051 by NAT_4:9;
    1051 = 23*45 + 16; hence not 23 divides 1051 by NAT_4:9;
    1051 = 29*36 + 7; hence not 29 divides 1051 by NAT_4:9;
    1051 = 31*33 + 28; hence not 31 divides 1051 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1051 & n is prime
  holds not n divides 1051 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
