
theorem
  6121 is prime
proof
  now
    6121 = 2*3060 + 1; hence not 2 divides 6121 by NAT_4:9;
    6121 = 3*2040 + 1; hence not 3 divides 6121 by NAT_4:9;
    6121 = 5*1224 + 1; hence not 5 divides 6121 by NAT_4:9;
    6121 = 7*874 + 3; hence not 7 divides 6121 by NAT_4:9;
    6121 = 11*556 + 5; hence not 11 divides 6121 by NAT_4:9;
    6121 = 13*470 + 11; hence not 13 divides 6121 by NAT_4:9;
    6121 = 17*360 + 1; hence not 17 divides 6121 by NAT_4:9;
    6121 = 19*322 + 3; hence not 19 divides 6121 by NAT_4:9;
    6121 = 23*266 + 3; hence not 23 divides 6121 by NAT_4:9;
    6121 = 29*211 + 2; hence not 29 divides 6121 by NAT_4:9;
    6121 = 31*197 + 14; hence not 31 divides 6121 by NAT_4:9;
    6121 = 37*165 + 16; hence not 37 divides 6121 by NAT_4:9;
    6121 = 41*149 + 12; hence not 41 divides 6121 by NAT_4:9;
    6121 = 43*142 + 15; hence not 43 divides 6121 by NAT_4:9;
    6121 = 47*130 + 11; hence not 47 divides 6121 by NAT_4:9;
    6121 = 53*115 + 26; hence not 53 divides 6121 by NAT_4:9;
    6121 = 59*103 + 44; hence not 59 divides 6121 by NAT_4:9;
    6121 = 61*100 + 21; hence not 61 divides 6121 by NAT_4:9;
    6121 = 67*91 + 24; hence not 67 divides 6121 by NAT_4:9;
    6121 = 71*86 + 15; hence not 71 divides 6121 by NAT_4:9;
    6121 = 73*83 + 62; hence not 73 divides 6121 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6121 & n is prime
  holds not n divides 6121 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
