
theorem
  4657 is prime
proof
  now
    4657 = 2*2328 + 1; hence not 2 divides 4657 by NAT_4:9;
    4657 = 3*1552 + 1; hence not 3 divides 4657 by NAT_4:9;
    4657 = 5*931 + 2; hence not 5 divides 4657 by NAT_4:9;
    4657 = 7*665 + 2; hence not 7 divides 4657 by NAT_4:9;
    4657 = 11*423 + 4; hence not 11 divides 4657 by NAT_4:9;
    4657 = 13*358 + 3; hence not 13 divides 4657 by NAT_4:9;
    4657 = 17*273 + 16; hence not 17 divides 4657 by NAT_4:9;
    4657 = 19*245 + 2; hence not 19 divides 4657 by NAT_4:9;
    4657 = 23*202 + 11; hence not 23 divides 4657 by NAT_4:9;
    4657 = 29*160 + 17; hence not 29 divides 4657 by NAT_4:9;
    4657 = 31*150 + 7; hence not 31 divides 4657 by NAT_4:9;
    4657 = 37*125 + 32; hence not 37 divides 4657 by NAT_4:9;
    4657 = 41*113 + 24; hence not 41 divides 4657 by NAT_4:9;
    4657 = 43*108 + 13; hence not 43 divides 4657 by NAT_4:9;
    4657 = 47*99 + 4; hence not 47 divides 4657 by NAT_4:9;
    4657 = 53*87 + 46; hence not 53 divides 4657 by NAT_4:9;
    4657 = 59*78 + 55; hence not 59 divides 4657 by NAT_4:9;
    4657 = 61*76 + 21; hence not 61 divides 4657 by NAT_4:9;
    4657 = 67*69 + 34; hence not 67 divides 4657 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4657 & n is prime
  holds not n divides 4657 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
