
theorem
  7753 is prime
proof
  now
    7753 = 2*3876 + 1; hence not 2 divides 7753 by NAT_4:9;
    7753 = 3*2584 + 1; hence not 3 divides 7753 by NAT_4:9;
    7753 = 5*1550 + 3; hence not 5 divides 7753 by NAT_4:9;
    7753 = 7*1107 + 4; hence not 7 divides 7753 by NAT_4:9;
    7753 = 11*704 + 9; hence not 11 divides 7753 by NAT_4:9;
    7753 = 13*596 + 5; hence not 13 divides 7753 by NAT_4:9;
    7753 = 17*456 + 1; hence not 17 divides 7753 by NAT_4:9;
    7753 = 19*408 + 1; hence not 19 divides 7753 by NAT_4:9;
    7753 = 23*337 + 2; hence not 23 divides 7753 by NAT_4:9;
    7753 = 29*267 + 10; hence not 29 divides 7753 by NAT_4:9;
    7753 = 31*250 + 3; hence not 31 divides 7753 by NAT_4:9;
    7753 = 37*209 + 20; hence not 37 divides 7753 by NAT_4:9;
    7753 = 41*189 + 4; hence not 41 divides 7753 by NAT_4:9;
    7753 = 43*180 + 13; hence not 43 divides 7753 by NAT_4:9;
    7753 = 47*164 + 45; hence not 47 divides 7753 by NAT_4:9;
    7753 = 53*146 + 15; hence not 53 divides 7753 by NAT_4:9;
    7753 = 59*131 + 24; hence not 59 divides 7753 by NAT_4:9;
    7753 = 61*127 + 6; hence not 61 divides 7753 by NAT_4:9;
    7753 = 67*115 + 48; hence not 67 divides 7753 by NAT_4:9;
    7753 = 71*109 + 14; hence not 71 divides 7753 by NAT_4:9;
    7753 = 73*106 + 15; hence not 73 divides 7753 by NAT_4:9;
    7753 = 79*98 + 11; hence not 79 divides 7753 by NAT_4:9;
    7753 = 83*93 + 34; hence not 83 divides 7753 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7753 & n is prime
  holds not n divides 7753 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
