
theorem
  7507 is prime
proof
  now
    7507 = 2*3753 + 1; hence not 2 divides 7507 by NAT_4:9;
    7507 = 3*2502 + 1; hence not 3 divides 7507 by NAT_4:9;
    7507 = 5*1501 + 2; hence not 5 divides 7507 by NAT_4:9;
    7507 = 7*1072 + 3; hence not 7 divides 7507 by NAT_4:9;
    7507 = 11*682 + 5; hence not 11 divides 7507 by NAT_4:9;
    7507 = 13*577 + 6; hence not 13 divides 7507 by NAT_4:9;
    7507 = 17*441 + 10; hence not 17 divides 7507 by NAT_4:9;
    7507 = 19*395 + 2; hence not 19 divides 7507 by NAT_4:9;
    7507 = 23*326 + 9; hence not 23 divides 7507 by NAT_4:9;
    7507 = 29*258 + 25; hence not 29 divides 7507 by NAT_4:9;
    7507 = 31*242 + 5; hence not 31 divides 7507 by NAT_4:9;
    7507 = 37*202 + 33; hence not 37 divides 7507 by NAT_4:9;
    7507 = 41*183 + 4; hence not 41 divides 7507 by NAT_4:9;
    7507 = 43*174 + 25; hence not 43 divides 7507 by NAT_4:9;
    7507 = 47*159 + 34; hence not 47 divides 7507 by NAT_4:9;
    7507 = 53*141 + 34; hence not 53 divides 7507 by NAT_4:9;
    7507 = 59*127 + 14; hence not 59 divides 7507 by NAT_4:9;
    7507 = 61*123 + 4; hence not 61 divides 7507 by NAT_4:9;
    7507 = 67*112 + 3; hence not 67 divides 7507 by NAT_4:9;
    7507 = 71*105 + 52; hence not 71 divides 7507 by NAT_4:9;
    7507 = 73*102 + 61; hence not 73 divides 7507 by NAT_4:9;
    7507 = 79*95 + 2; hence not 79 divides 7507 by NAT_4:9;
    7507 = 83*90 + 37; hence not 83 divides 7507 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7507 & n is prime
  holds not n divides 7507 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
