
theorem
  7529 is prime
proof
  now
    7529 = 2*3764 + 1; hence not 2 divides 7529 by NAT_4:9;
    7529 = 3*2509 + 2; hence not 3 divides 7529 by NAT_4:9;
    7529 = 5*1505 + 4; hence not 5 divides 7529 by NAT_4:9;
    7529 = 7*1075 + 4; hence not 7 divides 7529 by NAT_4:9;
    7529 = 11*684 + 5; hence not 11 divides 7529 by NAT_4:9;
    7529 = 13*579 + 2; hence not 13 divides 7529 by NAT_4:9;
    7529 = 17*442 + 15; hence not 17 divides 7529 by NAT_4:9;
    7529 = 19*396 + 5; hence not 19 divides 7529 by NAT_4:9;
    7529 = 23*327 + 8; hence not 23 divides 7529 by NAT_4:9;
    7529 = 29*259 + 18; hence not 29 divides 7529 by NAT_4:9;
    7529 = 31*242 + 27; hence not 31 divides 7529 by NAT_4:9;
    7529 = 37*203 + 18; hence not 37 divides 7529 by NAT_4:9;
    7529 = 41*183 + 26; hence not 41 divides 7529 by NAT_4:9;
    7529 = 43*175 + 4; hence not 43 divides 7529 by NAT_4:9;
    7529 = 47*160 + 9; hence not 47 divides 7529 by NAT_4:9;
    7529 = 53*142 + 3; hence not 53 divides 7529 by NAT_4:9;
    7529 = 59*127 + 36; hence not 59 divides 7529 by NAT_4:9;
    7529 = 61*123 + 26; hence not 61 divides 7529 by NAT_4:9;
    7529 = 67*112 + 25; hence not 67 divides 7529 by NAT_4:9;
    7529 = 71*106 + 3; hence not 71 divides 7529 by NAT_4:9;
    7529 = 73*103 + 10; hence not 73 divides 7529 by NAT_4:9;
    7529 = 79*95 + 24; hence not 79 divides 7529 by NAT_4:9;
    7529 = 83*90 + 59; hence not 83 divides 7529 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7529 & n is prime
  holds not n divides 7529 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
