
theorem
  6761 is prime
proof
  now
    6761 = 2*3380 + 1; hence not 2 divides 6761 by NAT_4:9;
    6761 = 3*2253 + 2; hence not 3 divides 6761 by NAT_4:9;
    6761 = 5*1352 + 1; hence not 5 divides 6761 by NAT_4:9;
    6761 = 7*965 + 6; hence not 7 divides 6761 by NAT_4:9;
    6761 = 11*614 + 7; hence not 11 divides 6761 by NAT_4:9;
    6761 = 13*520 + 1; hence not 13 divides 6761 by NAT_4:9;
    6761 = 17*397 + 12; hence not 17 divides 6761 by NAT_4:9;
    6761 = 19*355 + 16; hence not 19 divides 6761 by NAT_4:9;
    6761 = 23*293 + 22; hence not 23 divides 6761 by NAT_4:9;
    6761 = 29*233 + 4; hence not 29 divides 6761 by NAT_4:9;
    6761 = 31*218 + 3; hence not 31 divides 6761 by NAT_4:9;
    6761 = 37*182 + 27; hence not 37 divides 6761 by NAT_4:9;
    6761 = 41*164 + 37; hence not 41 divides 6761 by NAT_4:9;
    6761 = 43*157 + 10; hence not 43 divides 6761 by NAT_4:9;
    6761 = 47*143 + 40; hence not 47 divides 6761 by NAT_4:9;
    6761 = 53*127 + 30; hence not 53 divides 6761 by NAT_4:9;
    6761 = 59*114 + 35; hence not 59 divides 6761 by NAT_4:9;
    6761 = 61*110 + 51; hence not 61 divides 6761 by NAT_4:9;
    6761 = 67*100 + 61; hence not 67 divides 6761 by NAT_4:9;
    6761 = 71*95 + 16; hence not 71 divides 6761 by NAT_4:9;
    6761 = 73*92 + 45; hence not 73 divides 6761 by NAT_4:9;
    6761 = 79*85 + 46; hence not 79 divides 6761 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6761 & n is prime
  holds not n divides 6761 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
