
theorem
  5839 is prime
proof
  now
    5839 = 2*2919 + 1; hence not 2 divides 5839 by NAT_4:9;
    5839 = 3*1946 + 1; hence not 3 divides 5839 by NAT_4:9;
    5839 = 5*1167 + 4; hence not 5 divides 5839 by NAT_4:9;
    5839 = 7*834 + 1; hence not 7 divides 5839 by NAT_4:9;
    5839 = 11*530 + 9; hence not 11 divides 5839 by NAT_4:9;
    5839 = 13*449 + 2; hence not 13 divides 5839 by NAT_4:9;
    5839 = 17*343 + 8; hence not 17 divides 5839 by NAT_4:9;
    5839 = 19*307 + 6; hence not 19 divides 5839 by NAT_4:9;
    5839 = 23*253 + 20; hence not 23 divides 5839 by NAT_4:9;
    5839 = 29*201 + 10; hence not 29 divides 5839 by NAT_4:9;
    5839 = 31*188 + 11; hence not 31 divides 5839 by NAT_4:9;
    5839 = 37*157 + 30; hence not 37 divides 5839 by NAT_4:9;
    5839 = 41*142 + 17; hence not 41 divides 5839 by NAT_4:9;
    5839 = 43*135 + 34; hence not 43 divides 5839 by NAT_4:9;
    5839 = 47*124 + 11; hence not 47 divides 5839 by NAT_4:9;
    5839 = 53*110 + 9; hence not 53 divides 5839 by NAT_4:9;
    5839 = 59*98 + 57; hence not 59 divides 5839 by NAT_4:9;
    5839 = 61*95 + 44; hence not 61 divides 5839 by NAT_4:9;
    5839 = 67*87 + 10; hence not 67 divides 5839 by NAT_4:9;
    5839 = 71*82 + 17; hence not 71 divides 5839 by NAT_4:9;
    5839 = 73*79 + 72; hence not 73 divides 5839 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5839 & n is prime
  holds not n divides 5839 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
