
theorem
  6949 is prime
proof
  now
    6949 = 2*3474 + 1; hence not 2 divides 6949 by NAT_4:9;
    6949 = 3*2316 + 1; hence not 3 divides 6949 by NAT_4:9;
    6949 = 5*1389 + 4; hence not 5 divides 6949 by NAT_4:9;
    6949 = 7*992 + 5; hence not 7 divides 6949 by NAT_4:9;
    6949 = 11*631 + 8; hence not 11 divides 6949 by NAT_4:9;
    6949 = 13*534 + 7; hence not 13 divides 6949 by NAT_4:9;
    6949 = 17*408 + 13; hence not 17 divides 6949 by NAT_4:9;
    6949 = 19*365 + 14; hence not 19 divides 6949 by NAT_4:9;
    6949 = 23*302 + 3; hence not 23 divides 6949 by NAT_4:9;
    6949 = 29*239 + 18; hence not 29 divides 6949 by NAT_4:9;
    6949 = 31*224 + 5; hence not 31 divides 6949 by NAT_4:9;
    6949 = 37*187 + 30; hence not 37 divides 6949 by NAT_4:9;
    6949 = 41*169 + 20; hence not 41 divides 6949 by NAT_4:9;
    6949 = 43*161 + 26; hence not 43 divides 6949 by NAT_4:9;
    6949 = 47*147 + 40; hence not 47 divides 6949 by NAT_4:9;
    6949 = 53*131 + 6; hence not 53 divides 6949 by NAT_4:9;
    6949 = 59*117 + 46; hence not 59 divides 6949 by NAT_4:9;
    6949 = 61*113 + 56; hence not 61 divides 6949 by NAT_4:9;
    6949 = 67*103 + 48; hence not 67 divides 6949 by NAT_4:9;
    6949 = 71*97 + 62; hence not 71 divides 6949 by NAT_4:9;
    6949 = 73*95 + 14; hence not 73 divides 6949 by NAT_4:9;
    6949 = 79*87 + 76; hence not 79 divides 6949 by NAT_4:9;
    6949 = 83*83 + 60; hence not 83 divides 6949 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6949 & n is prime
  holds not n divides 6949 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
