
theorem
  7759 is prime
proof
  now
    7759 = 2*3879 + 1; hence not 2 divides 7759 by NAT_4:9;
    7759 = 3*2586 + 1; hence not 3 divides 7759 by NAT_4:9;
    7759 = 5*1551 + 4; hence not 5 divides 7759 by NAT_4:9;
    7759 = 7*1108 + 3; hence not 7 divides 7759 by NAT_4:9;
    7759 = 11*705 + 4; hence not 11 divides 7759 by NAT_4:9;
    7759 = 13*596 + 11; hence not 13 divides 7759 by NAT_4:9;
    7759 = 17*456 + 7; hence not 17 divides 7759 by NAT_4:9;
    7759 = 19*408 + 7; hence not 19 divides 7759 by NAT_4:9;
    7759 = 23*337 + 8; hence not 23 divides 7759 by NAT_4:9;
    7759 = 29*267 + 16; hence not 29 divides 7759 by NAT_4:9;
    7759 = 31*250 + 9; hence not 31 divides 7759 by NAT_4:9;
    7759 = 37*209 + 26; hence not 37 divides 7759 by NAT_4:9;
    7759 = 41*189 + 10; hence not 41 divides 7759 by NAT_4:9;
    7759 = 43*180 + 19; hence not 43 divides 7759 by NAT_4:9;
    7759 = 47*165 + 4; hence not 47 divides 7759 by NAT_4:9;
    7759 = 53*146 + 21; hence not 53 divides 7759 by NAT_4:9;
    7759 = 59*131 + 30; hence not 59 divides 7759 by NAT_4:9;
    7759 = 61*127 + 12; hence not 61 divides 7759 by NAT_4:9;
    7759 = 67*115 + 54; hence not 67 divides 7759 by NAT_4:9;
    7759 = 71*109 + 20; hence not 71 divides 7759 by NAT_4:9;
    7759 = 73*106 + 21; hence not 73 divides 7759 by NAT_4:9;
    7759 = 79*98 + 17; hence not 79 divides 7759 by NAT_4:9;
    7759 = 83*93 + 40; hence not 83 divides 7759 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7759 & n is prime
  holds not n divides 7759 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
