
theorem
  5857 is prime
proof
  now
    5857 = 2*2928 + 1; hence not 2 divides 5857 by NAT_4:9;
    5857 = 3*1952 + 1; hence not 3 divides 5857 by NAT_4:9;
    5857 = 5*1171 + 2; hence not 5 divides 5857 by NAT_4:9;
    5857 = 7*836 + 5; hence not 7 divides 5857 by NAT_4:9;
    5857 = 11*532 + 5; hence not 11 divides 5857 by NAT_4:9;
    5857 = 13*450 + 7; hence not 13 divides 5857 by NAT_4:9;
    5857 = 17*344 + 9; hence not 17 divides 5857 by NAT_4:9;
    5857 = 19*308 + 5; hence not 19 divides 5857 by NAT_4:9;
    5857 = 23*254 + 15; hence not 23 divides 5857 by NAT_4:9;
    5857 = 29*201 + 28; hence not 29 divides 5857 by NAT_4:9;
    5857 = 31*188 + 29; hence not 31 divides 5857 by NAT_4:9;
    5857 = 37*158 + 11; hence not 37 divides 5857 by NAT_4:9;
    5857 = 41*142 + 35; hence not 41 divides 5857 by NAT_4:9;
    5857 = 43*136 + 9; hence not 43 divides 5857 by NAT_4:9;
    5857 = 47*124 + 29; hence not 47 divides 5857 by NAT_4:9;
    5857 = 53*110 + 27; hence not 53 divides 5857 by NAT_4:9;
    5857 = 59*99 + 16; hence not 59 divides 5857 by NAT_4:9;
    5857 = 61*96 + 1; hence not 61 divides 5857 by NAT_4:9;
    5857 = 67*87 + 28; hence not 67 divides 5857 by NAT_4:9;
    5857 = 71*82 + 35; hence not 71 divides 5857 by NAT_4:9;
    5857 = 73*80 + 17; hence not 73 divides 5857 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5857 & n is prime
  holds not n divides 5857 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
