
theorem
  5147 is prime
proof
  now
    5147 = 2*2573 + 1; hence not 2 divides 5147 by NAT_4:9;
    5147 = 3*1715 + 2; hence not 3 divides 5147 by NAT_4:9;
    5147 = 5*1029 + 2; hence not 5 divides 5147 by NAT_4:9;
    5147 = 7*735 + 2; hence not 7 divides 5147 by NAT_4:9;
    5147 = 11*467 + 10; hence not 11 divides 5147 by NAT_4:9;
    5147 = 13*395 + 12; hence not 13 divides 5147 by NAT_4:9;
    5147 = 17*302 + 13; hence not 17 divides 5147 by NAT_4:9;
    5147 = 19*270 + 17; hence not 19 divides 5147 by NAT_4:9;
    5147 = 23*223 + 18; hence not 23 divides 5147 by NAT_4:9;
    5147 = 29*177 + 14; hence not 29 divides 5147 by NAT_4:9;
    5147 = 31*166 + 1; hence not 31 divides 5147 by NAT_4:9;
    5147 = 37*139 + 4; hence not 37 divides 5147 by NAT_4:9;
    5147 = 41*125 + 22; hence not 41 divides 5147 by NAT_4:9;
    5147 = 43*119 + 30; hence not 43 divides 5147 by NAT_4:9;
    5147 = 47*109 + 24; hence not 47 divides 5147 by NAT_4:9;
    5147 = 53*97 + 6; hence not 53 divides 5147 by NAT_4:9;
    5147 = 59*87 + 14; hence not 59 divides 5147 by NAT_4:9;
    5147 = 61*84 + 23; hence not 61 divides 5147 by NAT_4:9;
    5147 = 67*76 + 55; hence not 67 divides 5147 by NAT_4:9;
    5147 = 71*72 + 35; hence not 71 divides 5147 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5147 & n is prime
  holds not n divides 5147 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
