
theorem
  7589 is prime
proof
  now
    7589 = 2*3794 + 1; hence not 2 divides 7589 by NAT_4:9;
    7589 = 3*2529 + 2; hence not 3 divides 7589 by NAT_4:9;
    7589 = 5*1517 + 4; hence not 5 divides 7589 by NAT_4:9;
    7589 = 7*1084 + 1; hence not 7 divides 7589 by NAT_4:9;
    7589 = 11*689 + 10; hence not 11 divides 7589 by NAT_4:9;
    7589 = 13*583 + 10; hence not 13 divides 7589 by NAT_4:9;
    7589 = 17*446 + 7; hence not 17 divides 7589 by NAT_4:9;
    7589 = 19*399 + 8; hence not 19 divides 7589 by NAT_4:9;
    7589 = 23*329 + 22; hence not 23 divides 7589 by NAT_4:9;
    7589 = 29*261 + 20; hence not 29 divides 7589 by NAT_4:9;
    7589 = 31*244 + 25; hence not 31 divides 7589 by NAT_4:9;
    7589 = 37*205 + 4; hence not 37 divides 7589 by NAT_4:9;
    7589 = 41*185 + 4; hence not 41 divides 7589 by NAT_4:9;
    7589 = 43*176 + 21; hence not 43 divides 7589 by NAT_4:9;
    7589 = 47*161 + 22; hence not 47 divides 7589 by NAT_4:9;
    7589 = 53*143 + 10; hence not 53 divides 7589 by NAT_4:9;
    7589 = 59*128 + 37; hence not 59 divides 7589 by NAT_4:9;
    7589 = 61*124 + 25; hence not 61 divides 7589 by NAT_4:9;
    7589 = 67*113 + 18; hence not 67 divides 7589 by NAT_4:9;
    7589 = 71*106 + 63; hence not 71 divides 7589 by NAT_4:9;
    7589 = 73*103 + 70; hence not 73 divides 7589 by NAT_4:9;
    7589 = 79*96 + 5; hence not 79 divides 7589 by NAT_4:9;
    7589 = 83*91 + 36; hence not 83 divides 7589 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7589 & n is prime
  holds not n divides 7589 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
