
theorem
  7559 is prime
proof
  now
    7559 = 2*3779 + 1; hence not 2 divides 7559 by NAT_4:9;
    7559 = 3*2519 + 2; hence not 3 divides 7559 by NAT_4:9;
    7559 = 5*1511 + 4; hence not 5 divides 7559 by NAT_4:9;
    7559 = 7*1079 + 6; hence not 7 divides 7559 by NAT_4:9;
    7559 = 11*687 + 2; hence not 11 divides 7559 by NAT_4:9;
    7559 = 13*581 + 6; hence not 13 divides 7559 by NAT_4:9;
    7559 = 17*444 + 11; hence not 17 divides 7559 by NAT_4:9;
    7559 = 19*397 + 16; hence not 19 divides 7559 by NAT_4:9;
    7559 = 23*328 + 15; hence not 23 divides 7559 by NAT_4:9;
    7559 = 29*260 + 19; hence not 29 divides 7559 by NAT_4:9;
    7559 = 31*243 + 26; hence not 31 divides 7559 by NAT_4:9;
    7559 = 37*204 + 11; hence not 37 divides 7559 by NAT_4:9;
    7559 = 41*184 + 15; hence not 41 divides 7559 by NAT_4:9;
    7559 = 43*175 + 34; hence not 43 divides 7559 by NAT_4:9;
    7559 = 47*160 + 39; hence not 47 divides 7559 by NAT_4:9;
    7559 = 53*142 + 33; hence not 53 divides 7559 by NAT_4:9;
    7559 = 59*128 + 7; hence not 59 divides 7559 by NAT_4:9;
    7559 = 61*123 + 56; hence not 61 divides 7559 by NAT_4:9;
    7559 = 67*112 + 55; hence not 67 divides 7559 by NAT_4:9;
    7559 = 71*106 + 33; hence not 71 divides 7559 by NAT_4:9;
    7559 = 73*103 + 40; hence not 73 divides 7559 by NAT_4:9;
    7559 = 79*95 + 54; hence not 79 divides 7559 by NAT_4:9;
    7559 = 83*91 + 6; hence not 83 divides 7559 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7559 & n is prime
  holds not n divides 7559 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
