
theorem
  2657 is prime
proof
  now
    2657 = 2*1328 + 1; hence not 2 divides 2657 by NAT_4:9;
    2657 = 3*885 + 2; hence not 3 divides 2657 by NAT_4:9;
    2657 = 5*531 + 2; hence not 5 divides 2657 by NAT_4:9;
    2657 = 7*379 + 4; hence not 7 divides 2657 by NAT_4:9;
    2657 = 11*241 + 6; hence not 11 divides 2657 by NAT_4:9;
    2657 = 13*204 + 5; hence not 13 divides 2657 by NAT_4:9;
    2657 = 17*156 + 5; hence not 17 divides 2657 by NAT_4:9;
    2657 = 19*139 + 16; hence not 19 divides 2657 by NAT_4:9;
    2657 = 23*115 + 12; hence not 23 divides 2657 by NAT_4:9;
    2657 = 29*91 + 18; hence not 29 divides 2657 by NAT_4:9;
    2657 = 31*85 + 22; hence not 31 divides 2657 by NAT_4:9;
    2657 = 37*71 + 30; hence not 37 divides 2657 by NAT_4:9;
    2657 = 41*64 + 33; hence not 41 divides 2657 by NAT_4:9;
    2657 = 43*61 + 34; hence not 43 divides 2657 by NAT_4:9;
    2657 = 47*56 + 25; hence not 47 divides 2657 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2657 & n is prime
  holds not n divides 2657 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
