
theorem
  6101 is prime
proof
  now
    6101 = 2*3050 + 1; hence not 2 divides 6101 by NAT_4:9;
    6101 = 3*2033 + 2; hence not 3 divides 6101 by NAT_4:9;
    6101 = 5*1220 + 1; hence not 5 divides 6101 by NAT_4:9;
    6101 = 7*871 + 4; hence not 7 divides 6101 by NAT_4:9;
    6101 = 11*554 + 7; hence not 11 divides 6101 by NAT_4:9;
    6101 = 13*469 + 4; hence not 13 divides 6101 by NAT_4:9;
    6101 = 17*358 + 15; hence not 17 divides 6101 by NAT_4:9;
    6101 = 19*321 + 2; hence not 19 divides 6101 by NAT_4:9;
    6101 = 23*265 + 6; hence not 23 divides 6101 by NAT_4:9;
    6101 = 29*210 + 11; hence not 29 divides 6101 by NAT_4:9;
    6101 = 31*196 + 25; hence not 31 divides 6101 by NAT_4:9;
    6101 = 37*164 + 33; hence not 37 divides 6101 by NAT_4:9;
    6101 = 41*148 + 33; hence not 41 divides 6101 by NAT_4:9;
    6101 = 43*141 + 38; hence not 43 divides 6101 by NAT_4:9;
    6101 = 47*129 + 38; hence not 47 divides 6101 by NAT_4:9;
    6101 = 53*115 + 6; hence not 53 divides 6101 by NAT_4:9;
    6101 = 59*103 + 24; hence not 59 divides 6101 by NAT_4:9;
    6101 = 61*100 + 1; hence not 61 divides 6101 by NAT_4:9;
    6101 = 67*91 + 4; hence not 67 divides 6101 by NAT_4:9;
    6101 = 71*85 + 66; hence not 71 divides 6101 by NAT_4:9;
    6101 = 73*83 + 42; hence not 73 divides 6101 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6101 & n is prime
  holds not n divides 6101 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
