
theorem
  3659 is prime
proof
  now
    3659 = 2*1829 + 1; hence not 2 divides 3659 by NAT_4:9;
    3659 = 3*1219 + 2; hence not 3 divides 3659 by NAT_4:9;
    3659 = 5*731 + 4; hence not 5 divides 3659 by NAT_4:9;
    3659 = 7*522 + 5; hence not 7 divides 3659 by NAT_4:9;
    3659 = 11*332 + 7; hence not 11 divides 3659 by NAT_4:9;
    3659 = 13*281 + 6; hence not 13 divides 3659 by NAT_4:9;
    3659 = 17*215 + 4; hence not 17 divides 3659 by NAT_4:9;
    3659 = 19*192 + 11; hence not 19 divides 3659 by NAT_4:9;
    3659 = 23*159 + 2; hence not 23 divides 3659 by NAT_4:9;
    3659 = 29*126 + 5; hence not 29 divides 3659 by NAT_4:9;
    3659 = 31*118 + 1; hence not 31 divides 3659 by NAT_4:9;
    3659 = 37*98 + 33; hence not 37 divides 3659 by NAT_4:9;
    3659 = 41*89 + 10; hence not 41 divides 3659 by NAT_4:9;
    3659 = 43*85 + 4; hence not 43 divides 3659 by NAT_4:9;
    3659 = 47*77 + 40; hence not 47 divides 3659 by NAT_4:9;
    3659 = 53*69 + 2; hence not 53 divides 3659 by NAT_4:9;
    3659 = 59*62 + 1; hence not 59 divides 3659 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3659 & n is prime
  holds not n divides 3659 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
