
theorem
  7583 is prime
proof
  now
    7583 = 2*3791 + 1; hence not 2 divides 7583 by NAT_4:9;
    7583 = 3*2527 + 2; hence not 3 divides 7583 by NAT_4:9;
    7583 = 5*1516 + 3; hence not 5 divides 7583 by NAT_4:9;
    7583 = 7*1083 + 2; hence not 7 divides 7583 by NAT_4:9;
    7583 = 11*689 + 4; hence not 11 divides 7583 by NAT_4:9;
    7583 = 13*583 + 4; hence not 13 divides 7583 by NAT_4:9;
    7583 = 17*446 + 1; hence not 17 divides 7583 by NAT_4:9;
    7583 = 19*399 + 2; hence not 19 divides 7583 by NAT_4:9;
    7583 = 23*329 + 16; hence not 23 divides 7583 by NAT_4:9;
    7583 = 29*261 + 14; hence not 29 divides 7583 by NAT_4:9;
    7583 = 31*244 + 19; hence not 31 divides 7583 by NAT_4:9;
    7583 = 37*204 + 35; hence not 37 divides 7583 by NAT_4:9;
    7583 = 41*184 + 39; hence not 41 divides 7583 by NAT_4:9;
    7583 = 43*176 + 15; hence not 43 divides 7583 by NAT_4:9;
    7583 = 47*161 + 16; hence not 47 divides 7583 by NAT_4:9;
    7583 = 53*143 + 4; hence not 53 divides 7583 by NAT_4:9;
    7583 = 59*128 + 31; hence not 59 divides 7583 by NAT_4:9;
    7583 = 61*124 + 19; hence not 61 divides 7583 by NAT_4:9;
    7583 = 67*113 + 12; hence not 67 divides 7583 by NAT_4:9;
    7583 = 71*106 + 57; hence not 71 divides 7583 by NAT_4:9;
    7583 = 73*103 + 64; hence not 73 divides 7583 by NAT_4:9;
    7583 = 79*95 + 78; hence not 79 divides 7583 by NAT_4:9;
    7583 = 83*91 + 30; hence not 83 divides 7583 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7583 & n is prime
  holds not n divides 7583 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
