
theorem
  2851 is prime
proof
  now
    2851 = 2*1425 + 1; hence not 2 divides 2851 by NAT_4:9;
    2851 = 3*950 + 1; hence not 3 divides 2851 by NAT_4:9;
    2851 = 5*570 + 1; hence not 5 divides 2851 by NAT_4:9;
    2851 = 7*407 + 2; hence not 7 divides 2851 by NAT_4:9;
    2851 = 11*259 + 2; hence not 11 divides 2851 by NAT_4:9;
    2851 = 13*219 + 4; hence not 13 divides 2851 by NAT_4:9;
    2851 = 17*167 + 12; hence not 17 divides 2851 by NAT_4:9;
    2851 = 19*150 + 1; hence not 19 divides 2851 by NAT_4:9;
    2851 = 23*123 + 22; hence not 23 divides 2851 by NAT_4:9;
    2851 = 29*98 + 9; hence not 29 divides 2851 by NAT_4:9;
    2851 = 31*91 + 30; hence not 31 divides 2851 by NAT_4:9;
    2851 = 37*77 + 2; hence not 37 divides 2851 by NAT_4:9;
    2851 = 41*69 + 22; hence not 41 divides 2851 by NAT_4:9;
    2851 = 43*66 + 13; hence not 43 divides 2851 by NAT_4:9;
    2851 = 47*60 + 31; hence not 47 divides 2851 by NAT_4:9;
    2851 = 53*53 + 42; hence not 53 divides 2851 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2851 & n is prime
  holds not n divides 2851 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
