
theorem
  5851 is prime
proof
  now
    5851 = 2*2925 + 1; hence not 2 divides 5851 by NAT_4:9;
    5851 = 3*1950 + 1; hence not 3 divides 5851 by NAT_4:9;
    5851 = 5*1170 + 1; hence not 5 divides 5851 by NAT_4:9;
    5851 = 7*835 + 6; hence not 7 divides 5851 by NAT_4:9;
    5851 = 11*531 + 10; hence not 11 divides 5851 by NAT_4:9;
    5851 = 13*450 + 1; hence not 13 divides 5851 by NAT_4:9;
    5851 = 17*344 + 3; hence not 17 divides 5851 by NAT_4:9;
    5851 = 19*307 + 18; hence not 19 divides 5851 by NAT_4:9;
    5851 = 23*254 + 9; hence not 23 divides 5851 by NAT_4:9;
    5851 = 29*201 + 22; hence not 29 divides 5851 by NAT_4:9;
    5851 = 31*188 + 23; hence not 31 divides 5851 by NAT_4:9;
    5851 = 37*158 + 5; hence not 37 divides 5851 by NAT_4:9;
    5851 = 41*142 + 29; hence not 41 divides 5851 by NAT_4:9;
    5851 = 43*136 + 3; hence not 43 divides 5851 by NAT_4:9;
    5851 = 47*124 + 23; hence not 47 divides 5851 by NAT_4:9;
    5851 = 53*110 + 21; hence not 53 divides 5851 by NAT_4:9;
    5851 = 59*99 + 10; hence not 59 divides 5851 by NAT_4:9;
    5851 = 61*95 + 56; hence not 61 divides 5851 by NAT_4:9;
    5851 = 67*87 + 22; hence not 67 divides 5851 by NAT_4:9;
    5851 = 71*82 + 29; hence not 71 divides 5851 by NAT_4:9;
    5851 = 73*80 + 11; hence not 73 divides 5851 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5851 & n is prime
  holds not n divides 5851 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
