
theorem
  2861 is prime
proof
  now
    2861 = 2*1430 + 1; hence not 2 divides 2861 by NAT_4:9;
    2861 = 3*953 + 2; hence not 3 divides 2861 by NAT_4:9;
    2861 = 5*572 + 1; hence not 5 divides 2861 by NAT_4:9;
    2861 = 7*408 + 5; hence not 7 divides 2861 by NAT_4:9;
    2861 = 11*260 + 1; hence not 11 divides 2861 by NAT_4:9;
    2861 = 13*220 + 1; hence not 13 divides 2861 by NAT_4:9;
    2861 = 17*168 + 5; hence not 17 divides 2861 by NAT_4:9;
    2861 = 19*150 + 11; hence not 19 divides 2861 by NAT_4:9;
    2861 = 23*124 + 9; hence not 23 divides 2861 by NAT_4:9;
    2861 = 29*98 + 19; hence not 29 divides 2861 by NAT_4:9;
    2861 = 31*92 + 9; hence not 31 divides 2861 by NAT_4:9;
    2861 = 37*77 + 12; hence not 37 divides 2861 by NAT_4:9;
    2861 = 41*69 + 32; hence not 41 divides 2861 by NAT_4:9;
    2861 = 43*66 + 23; hence not 43 divides 2861 by NAT_4:9;
    2861 = 47*60 + 41; hence not 47 divides 2861 by NAT_4:9;
    2861 = 53*53 + 52; hence not 53 divides 2861 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2861 & n is prime
  holds not n divides 2861 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
