
theorem
  6961 is prime
proof
  now
    6961 = 2*3480 + 1; hence not 2 divides 6961 by NAT_4:9;
    6961 = 3*2320 + 1; hence not 3 divides 6961 by NAT_4:9;
    6961 = 5*1392 + 1; hence not 5 divides 6961 by NAT_4:9;
    6961 = 7*994 + 3; hence not 7 divides 6961 by NAT_4:9;
    6961 = 11*632 + 9; hence not 11 divides 6961 by NAT_4:9;
    6961 = 13*535 + 6; hence not 13 divides 6961 by NAT_4:9;
    6961 = 17*409 + 8; hence not 17 divides 6961 by NAT_4:9;
    6961 = 19*366 + 7; hence not 19 divides 6961 by NAT_4:9;
    6961 = 23*302 + 15; hence not 23 divides 6961 by NAT_4:9;
    6961 = 29*240 + 1; hence not 29 divides 6961 by NAT_4:9;
    6961 = 31*224 + 17; hence not 31 divides 6961 by NAT_4:9;
    6961 = 37*188 + 5; hence not 37 divides 6961 by NAT_4:9;
    6961 = 41*169 + 32; hence not 41 divides 6961 by NAT_4:9;
    6961 = 43*161 + 38; hence not 43 divides 6961 by NAT_4:9;
    6961 = 47*148 + 5; hence not 47 divides 6961 by NAT_4:9;
    6961 = 53*131 + 18; hence not 53 divides 6961 by NAT_4:9;
    6961 = 59*117 + 58; hence not 59 divides 6961 by NAT_4:9;
    6961 = 61*114 + 7; hence not 61 divides 6961 by NAT_4:9;
    6961 = 67*103 + 60; hence not 67 divides 6961 by NAT_4:9;
    6961 = 71*98 + 3; hence not 71 divides 6961 by NAT_4:9;
    6961 = 73*95 + 26; hence not 73 divides 6961 by NAT_4:9;
    6961 = 79*88 + 9; hence not 79 divides 6961 by NAT_4:9;
    6961 = 83*83 + 72; hence not 83 divides 6961 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6961 & n is prime
  holds not n divides 6961 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
