
theorem
  4637 is prime
proof
  now
    4637 = 2*2318 + 1; hence not 2 divides 4637 by NAT_4:9;
    4637 = 3*1545 + 2; hence not 3 divides 4637 by NAT_4:9;
    4637 = 5*927 + 2; hence not 5 divides 4637 by NAT_4:9;
    4637 = 7*662 + 3; hence not 7 divides 4637 by NAT_4:9;
    4637 = 11*421 + 6; hence not 11 divides 4637 by NAT_4:9;
    4637 = 13*356 + 9; hence not 13 divides 4637 by NAT_4:9;
    4637 = 17*272 + 13; hence not 17 divides 4637 by NAT_4:9;
    4637 = 19*244 + 1; hence not 19 divides 4637 by NAT_4:9;
    4637 = 23*201 + 14; hence not 23 divides 4637 by NAT_4:9;
    4637 = 29*159 + 26; hence not 29 divides 4637 by NAT_4:9;
    4637 = 31*149 + 18; hence not 31 divides 4637 by NAT_4:9;
    4637 = 37*125 + 12; hence not 37 divides 4637 by NAT_4:9;
    4637 = 41*113 + 4; hence not 41 divides 4637 by NAT_4:9;
    4637 = 43*107 + 36; hence not 43 divides 4637 by NAT_4:9;
    4637 = 47*98 + 31; hence not 47 divides 4637 by NAT_4:9;
    4637 = 53*87 + 26; hence not 53 divides 4637 by NAT_4:9;
    4637 = 59*78 + 35; hence not 59 divides 4637 by NAT_4:9;
    4637 = 61*76 + 1; hence not 61 divides 4637 by NAT_4:9;
    4637 = 67*69 + 14; hence not 67 divides 4637 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4637 & n is prime
  holds not n divides 4637 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
