
theorem
  5657 is prime
proof
  now
    5657 = 2*2828 + 1; hence not 2 divides 5657 by NAT_4:9;
    5657 = 3*1885 + 2; hence not 3 divides 5657 by NAT_4:9;
    5657 = 5*1131 + 2; hence not 5 divides 5657 by NAT_4:9;
    5657 = 7*808 + 1; hence not 7 divides 5657 by NAT_4:9;
    5657 = 11*514 + 3; hence not 11 divides 5657 by NAT_4:9;
    5657 = 13*435 + 2; hence not 13 divides 5657 by NAT_4:9;
    5657 = 17*332 + 13; hence not 17 divides 5657 by NAT_4:9;
    5657 = 19*297 + 14; hence not 19 divides 5657 by NAT_4:9;
    5657 = 23*245 + 22; hence not 23 divides 5657 by NAT_4:9;
    5657 = 29*195 + 2; hence not 29 divides 5657 by NAT_4:9;
    5657 = 31*182 + 15; hence not 31 divides 5657 by NAT_4:9;
    5657 = 37*152 + 33; hence not 37 divides 5657 by NAT_4:9;
    5657 = 41*137 + 40; hence not 41 divides 5657 by NAT_4:9;
    5657 = 43*131 + 24; hence not 43 divides 5657 by NAT_4:9;
    5657 = 47*120 + 17; hence not 47 divides 5657 by NAT_4:9;
    5657 = 53*106 + 39; hence not 53 divides 5657 by NAT_4:9;
    5657 = 59*95 + 52; hence not 59 divides 5657 by NAT_4:9;
    5657 = 61*92 + 45; hence not 61 divides 5657 by NAT_4:9;
    5657 = 67*84 + 29; hence not 67 divides 5657 by NAT_4:9;
    5657 = 71*79 + 48; hence not 71 divides 5657 by NAT_4:9;
    5657 = 73*77 + 36; hence not 73 divides 5657 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5657 & n is prime
  holds not n divides 5657 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
