
theorem
  5659 is prime
proof
  now
    5659 = 2*2829 + 1; hence not 2 divides 5659 by NAT_4:9;
    5659 = 3*1886 + 1; hence not 3 divides 5659 by NAT_4:9;
    5659 = 5*1131 + 4; hence not 5 divides 5659 by NAT_4:9;
    5659 = 7*808 + 3; hence not 7 divides 5659 by NAT_4:9;
    5659 = 11*514 + 5; hence not 11 divides 5659 by NAT_4:9;
    5659 = 13*435 + 4; hence not 13 divides 5659 by NAT_4:9;
    5659 = 17*332 + 15; hence not 17 divides 5659 by NAT_4:9;
    5659 = 19*297 + 16; hence not 19 divides 5659 by NAT_4:9;
    5659 = 23*246 + 1; hence not 23 divides 5659 by NAT_4:9;
    5659 = 29*195 + 4; hence not 29 divides 5659 by NAT_4:9;
    5659 = 31*182 + 17; hence not 31 divides 5659 by NAT_4:9;
    5659 = 37*152 + 35; hence not 37 divides 5659 by NAT_4:9;
    5659 = 41*138 + 1; hence not 41 divides 5659 by NAT_4:9;
    5659 = 43*131 + 26; hence not 43 divides 5659 by NAT_4:9;
    5659 = 47*120 + 19; hence not 47 divides 5659 by NAT_4:9;
    5659 = 53*106 + 41; hence not 53 divides 5659 by NAT_4:9;
    5659 = 59*95 + 54; hence not 59 divides 5659 by NAT_4:9;
    5659 = 61*92 + 47; hence not 61 divides 5659 by NAT_4:9;
    5659 = 67*84 + 31; hence not 67 divides 5659 by NAT_4:9;
    5659 = 71*79 + 50; hence not 71 divides 5659 by NAT_4:9;
    5659 = 73*77 + 38; hence not 73 divides 5659 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5659 & n is prime
  holds not n divides 5659 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
