
theorem
  5431 is prime
proof
  now
    5431 = 2*2715 + 1; hence not 2 divides 5431 by NAT_4:9;
    5431 = 3*1810 + 1; hence not 3 divides 5431 by NAT_4:9;
    5431 = 5*1086 + 1; hence not 5 divides 5431 by NAT_4:9;
    5431 = 7*775 + 6; hence not 7 divides 5431 by NAT_4:9;
    5431 = 11*493 + 8; hence not 11 divides 5431 by NAT_4:9;
    5431 = 13*417 + 10; hence not 13 divides 5431 by NAT_4:9;
    5431 = 17*319 + 8; hence not 17 divides 5431 by NAT_4:9;
    5431 = 19*285 + 16; hence not 19 divides 5431 by NAT_4:9;
    5431 = 23*236 + 3; hence not 23 divides 5431 by NAT_4:9;
    5431 = 29*187 + 8; hence not 29 divides 5431 by NAT_4:9;
    5431 = 31*175 + 6; hence not 31 divides 5431 by NAT_4:9;
    5431 = 37*146 + 29; hence not 37 divides 5431 by NAT_4:9;
    5431 = 41*132 + 19; hence not 41 divides 5431 by NAT_4:9;
    5431 = 43*126 + 13; hence not 43 divides 5431 by NAT_4:9;
    5431 = 47*115 + 26; hence not 47 divides 5431 by NAT_4:9;
    5431 = 53*102 + 25; hence not 53 divides 5431 by NAT_4:9;
    5431 = 59*92 + 3; hence not 59 divides 5431 by NAT_4:9;
    5431 = 61*89 + 2; hence not 61 divides 5431 by NAT_4:9;
    5431 = 67*81 + 4; hence not 67 divides 5431 by NAT_4:9;
    5431 = 71*76 + 35; hence not 71 divides 5431 by NAT_4:9;
    5431 = 73*74 + 29; hence not 73 divides 5431 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5431 & n is prime
  holds not n divides 5431 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
