
theorem
  5653 is prime
proof
  now
    5653 = 2*2826 + 1; hence not 2 divides 5653 by NAT_4:9;
    5653 = 3*1884 + 1; hence not 3 divides 5653 by NAT_4:9;
    5653 = 5*1130 + 3; hence not 5 divides 5653 by NAT_4:9;
    5653 = 7*807 + 4; hence not 7 divides 5653 by NAT_4:9;
    5653 = 11*513 + 10; hence not 11 divides 5653 by NAT_4:9;
    5653 = 13*434 + 11; hence not 13 divides 5653 by NAT_4:9;
    5653 = 17*332 + 9; hence not 17 divides 5653 by NAT_4:9;
    5653 = 19*297 + 10; hence not 19 divides 5653 by NAT_4:9;
    5653 = 23*245 + 18; hence not 23 divides 5653 by NAT_4:9;
    5653 = 29*194 + 27; hence not 29 divides 5653 by NAT_4:9;
    5653 = 31*182 + 11; hence not 31 divides 5653 by NAT_4:9;
    5653 = 37*152 + 29; hence not 37 divides 5653 by NAT_4:9;
    5653 = 41*137 + 36; hence not 41 divides 5653 by NAT_4:9;
    5653 = 43*131 + 20; hence not 43 divides 5653 by NAT_4:9;
    5653 = 47*120 + 13; hence not 47 divides 5653 by NAT_4:9;
    5653 = 53*106 + 35; hence not 53 divides 5653 by NAT_4:9;
    5653 = 59*95 + 48; hence not 59 divides 5653 by NAT_4:9;
    5653 = 61*92 + 41; hence not 61 divides 5653 by NAT_4:9;
    5653 = 67*84 + 25; hence not 67 divides 5653 by NAT_4:9;
    5653 = 71*79 + 44; hence not 71 divides 5653 by NAT_4:9;
    5653 = 73*77 + 32; hence not 73 divides 5653 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5653 & n is prime
  holds not n divides 5653 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
