
theorem
  5861 is prime
proof
  now
    5861 = 2*2930 + 1; hence not 2 divides 5861 by NAT_4:9;
    5861 = 3*1953 + 2; hence not 3 divides 5861 by NAT_4:9;
    5861 = 5*1172 + 1; hence not 5 divides 5861 by NAT_4:9;
    5861 = 7*837 + 2; hence not 7 divides 5861 by NAT_4:9;
    5861 = 11*532 + 9; hence not 11 divides 5861 by NAT_4:9;
    5861 = 13*450 + 11; hence not 13 divides 5861 by NAT_4:9;
    5861 = 17*344 + 13; hence not 17 divides 5861 by NAT_4:9;
    5861 = 19*308 + 9; hence not 19 divides 5861 by NAT_4:9;
    5861 = 23*254 + 19; hence not 23 divides 5861 by NAT_4:9;
    5861 = 29*202 + 3; hence not 29 divides 5861 by NAT_4:9;
    5861 = 31*189 + 2; hence not 31 divides 5861 by NAT_4:9;
    5861 = 37*158 + 15; hence not 37 divides 5861 by NAT_4:9;
    5861 = 41*142 + 39; hence not 41 divides 5861 by NAT_4:9;
    5861 = 43*136 + 13; hence not 43 divides 5861 by NAT_4:9;
    5861 = 47*124 + 33; hence not 47 divides 5861 by NAT_4:9;
    5861 = 53*110 + 31; hence not 53 divides 5861 by NAT_4:9;
    5861 = 59*99 + 20; hence not 59 divides 5861 by NAT_4:9;
    5861 = 61*96 + 5; hence not 61 divides 5861 by NAT_4:9;
    5861 = 67*87 + 32; hence not 67 divides 5861 by NAT_4:9;
    5861 = 71*82 + 39; hence not 71 divides 5861 by NAT_4:9;
    5861 = 73*80 + 21; hence not 73 divides 5861 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5861 & n is prime
  holds not n divides 5861 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
