
theorem
  7607 is prime
proof
  now
    7607 = 2*3803 + 1; hence not 2 divides 7607 by NAT_4:9;
    7607 = 3*2535 + 2; hence not 3 divides 7607 by NAT_4:9;
    7607 = 5*1521 + 2; hence not 5 divides 7607 by NAT_4:9;
    7607 = 7*1086 + 5; hence not 7 divides 7607 by NAT_4:9;
    7607 = 11*691 + 6; hence not 11 divides 7607 by NAT_4:9;
    7607 = 13*585 + 2; hence not 13 divides 7607 by NAT_4:9;
    7607 = 17*447 + 8; hence not 17 divides 7607 by NAT_4:9;
    7607 = 19*400 + 7; hence not 19 divides 7607 by NAT_4:9;
    7607 = 23*330 + 17; hence not 23 divides 7607 by NAT_4:9;
    7607 = 29*262 + 9; hence not 29 divides 7607 by NAT_4:9;
    7607 = 31*245 + 12; hence not 31 divides 7607 by NAT_4:9;
    7607 = 37*205 + 22; hence not 37 divides 7607 by NAT_4:9;
    7607 = 41*185 + 22; hence not 41 divides 7607 by NAT_4:9;
    7607 = 43*176 + 39; hence not 43 divides 7607 by NAT_4:9;
    7607 = 47*161 + 40; hence not 47 divides 7607 by NAT_4:9;
    7607 = 53*143 + 28; hence not 53 divides 7607 by NAT_4:9;
    7607 = 59*128 + 55; hence not 59 divides 7607 by NAT_4:9;
    7607 = 61*124 + 43; hence not 61 divides 7607 by NAT_4:9;
    7607 = 67*113 + 36; hence not 67 divides 7607 by NAT_4:9;
    7607 = 71*107 + 10; hence not 71 divides 7607 by NAT_4:9;
    7607 = 73*104 + 15; hence not 73 divides 7607 by NAT_4:9;
    7607 = 79*96 + 23; hence not 79 divides 7607 by NAT_4:9;
    7607 = 83*91 + 54; hence not 83 divides 7607 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7607 & n is prime
  holds not n divides 7607 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
