M E R S E N N E   C A N D I D A T E   S I E V E       h o n e s t   c e r t a i n t y   e d i t i o n 
 
 
 
 = = =   M E R S E N N E   C A N D I D A T E   S I E V E   = = = 
 
 A n c h o r :   p = 2 5 0 0 0 0 0 0     o m e g a = 3 6 . 1 5 7 3 0 1 7 8 9 4 4 3     D = 5 
 
 S w e e p :     o m e g a   ,%%  0 . 0 0 4 0     s t e p s = 2 0 0 0 
 
 T r i a l   f a c t o r   l i m i t :   2 ^ 4 2 . 0   =   4 3 9 8 0 4 6 5 1 1 1 0 4 
 
 
 
 G e n e r a t e d   1 0 0 0   c a n d i d a t e   e x p o n e n t s   a b o v e   a n c h o r . 
 
 R u n n i n g   s i e v e . . . 
 
 
 
 
 
     P r o c e s s e d   5 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   1 0 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   1 5 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   2 0 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   2 5 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   3 0 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   3 5 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   4 0 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   4 5 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   5 0 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   5 5 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   6 0 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   6 5 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   7 0 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   7 5 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   8 0 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   8 5 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   9 0 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   9 5 0 / 1 0 0 0   . . . 
 
     P r o c e s s e d   1 0 0 0 / 1 0 0 0   . . . 
 
 
 
 = = =   S I E V E   R E S U L T S   = = = 
 
 T o t a l   c a n d i d a t e s :   1 0 0 0 
 
 E l i m i n a t e d   ( p   c o m p o s i t e ) :           9 4 9 
 
 E l i m i n a t e d   ( f a c t o r   f o u n d ) :         1 7 
 
 S u r v i v e d   ( n o   f a c t o r   t o   2 ^ 4 2 . 0 ) :   3 4 
 
 
 
 = = =   C E R T A I N T Y   S T A T E M E N T   = = = 
 
 C O M P O S I T E   r e s u l t s   a r e   1 0 0 %   c e r t a i n . 
 
 S U R V I V E D   r e s u l t s :   n o   f a c t o r   q   =   2 k p + 1   ( q       1 , 7   m o d   8 )   b e l o w   2 ^ 4 2 . 0 . 
 
 T h i s   d o e s   N O T   i m p l y   p r i m a l i t y .   S u r v i v i n g   c a n d i d a t e s   n e e d : 
 
         G P U   t r i a l   f a c t o r i n g   t o   2 ^ 7 6   ( m f a c t o r / G I M P S ) 
 
         F u l l   L u c a s - L e h m e r   t e s t   ( g p u o w l / m l u c a s ,   m o n t h s   o n   G P U ) 
 
 P L N   s c o r e s   a r e   H E U R I S T I C   R A N K I N G S   o n l y ,   n o t   p r i m a l i t y   e v i d e n c e . 
 
 
 
 = = =   T O P   S U R V I V O R S   ( r a n k e d   b y   P L N   s c o r e )   = = = 
 
     T h e s e   a r e   t h e   b e s t   c a n d i d a t e s   t o   s u b m i t   t o   g p u o w l : 
 
 
 
         1     p = 2 5 0 0 0 1 6 9                 D 5     g% = 3 6 . 1 5 7 3 1 5 8 4     d i g i t s = 7 5 2 5 8 0 1 
 
               s c o r e = 0 . 7 4 9 9 8     | R | = 2 . 3 0 0 0 5     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
         2     p = 2 5 0 0 0 8 9 1                 D 5     g% = 3 6 . 1 5 7 3 7 5 8 5     d i g i t s = 7 5 2 6 0 1 9 
 
               s c o r e = 0 . 7 4 9 9 1     | R | = 2 . 2 9 9 8 4     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
         3     p = 2 5 0 0 2 1 4 3                 D 5     g% = 3 6 . 1 5 7 4 7 9 9 2     d i g i t s = 7 5 2 6 3 9 5 
 
               s c o r e = 0 . 7 4 9 7 8     | R | = 2 . 2 9 9 4 7     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
         4     p = 2 5 0 0 2 1 9 1                 D 5     g% = 3 6 . 1 5 7 4 8 3 9 1     d i g i t s = 7 5 2 6 4 1 0 
 
               s c o r e = 0 . 7 4 9 7 8     | R | = 2 . 2 9 9 4 5     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
         5     p = 2 5 0 0 4 0 6 9                 D 5     g% = 3 6 . 1 5 7 6 3 9 9 9     d i g i t s = 7 5 2 6 9 7 5 
 
               s c o r e = 0 . 7 4 9 5 9     | R | = 2 . 2 9 8 8 9     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
         6     p = 2 5 0 0 4 8 3 9                 D 5     g% = 3 6 . 1 5 7 7 0 3 9 9     d i g i t s = 7 5 2 7 2 0 7 
 
               s c o r e = 0 . 7 4 9 5 1     | R | = 2 . 2 9 8 6 7     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
         7     p = 2 5 0 0 5 9 4 7                 D 5     g% = 3 6 . 1 5 7 7 9 6 0 7     d i g i t s = 7 5 2 7 5 4 1 
 
               s c o r e = 0 . 7 4 9 4 0     | R | = 2 . 2 9 8 3 4     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
         8     p = 2 5 0 0 6 6 2 1                 D 5     g% = 3 6 . 1 5 7 8 5 2 0 8     d i g i t s = 7 5 2 7 7 4 4 
 
               s c o r e = 0 . 7 4 9 3 3     | R | = 2 . 2 9 8 1 3     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
         9     p = 2 5 0 0 7 7 2 9                 D 5     g% = 3 6 . 1 5 7 9 4 4 1 5     d i g i t s = 7 5 2 8 0 7 7 
 
               s c o r e = 0 . 7 4 9 2 2     | R | = 2 . 2 9 7 8 0     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
       1 0     p = 2 5 0 0 8 0 1 7                 D 5     g% = 3 6 . 1 5 7 9 6 8 0 8     d i g i t s = 7 5 2 8 1 6 4 
 
               s c o r e = 0 . 7 4 9 1 9     | R | = 2 . 2 9 7 7 2     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
       1 1     p = 2 5 0 1 3 1 2 3                 D 5     g% = 3 6 . 1 5 8 3 9 2 3 3     d i g i t s = 7 5 2 9 7 0 1 
 
               s c o r e = 0 . 7 4 8 6 8     | R | = 2 . 2 9 6 2 0     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
       1 2     p = 2 5 0 1 5 3 3 9                 D 5     g% = 3 6 . 1 5 8 5 7 6 4 3     d i g i t s = 7 5 3 0 3 6 8 
 
               s c o r e = 0 . 7 4 8 4 5     | R | = 2 . 2 9 5 5 3     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
       1 3     p = 2 5 0 1 6 5 4 3                 D 5     g% = 3 6 . 1 5 8 6 7 6 4 5     d i g i t s = 7 5 3 0 7 3 0 
 
               s c o r e = 0 . 7 4 8 3 3     | R | = 2 . 2 9 5 1 7     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
       1 4     p = 2 5 0 1 7 0 7 3                 D 5     g% = 3 6 . 1 5 8 7 2 0 4 7     d i g i t s = 7 5 3 0 8 9 0 
 
               s c o r e = 0 . 7 4 8 2 8     | R | = 2 . 2 9 5 0 2     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
       1 5     p = 2 5 0 2 1 1 6 9                 D 5     g% = 3 6 . 1 5 9 0 6 0 6 9     d i g i t s = 7 5 3 2 1 2 3 
 
               s c o r e = 0 . 7 4 7 8 7     | R | = 2 . 2 9 3 7 9     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
       1 6     p = 2 5 0 2 3 2 8 9                 D 5     g% = 3 6 . 1 5 9 2 3 6 7 5     d i g i t s = 7 5 3 2 7 6 1 
 
               s c o r e = 0 . 7 4 7 6 5     | R | = 2 . 2 9 3 1 5     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
       1 7     p = 2 5 0 2 4 3 0 1                 D 5     g% = 3 6 . 1 5 9 3 2 0 7 9     d i g i t s = 7 5 3 3 0 6 6 
 
               s c o r e = 0 . 7 4 7 5 5     | R | = 2 . 2 9 2 8 5     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
       1 8     p = 2 5 0 2 5 8 4 3                 D 5     g% = 3 6 . 1 5 9 4 4 8 8 4     d i g i t s = 7 5 3 3 5 3 0 
 
               s c o r e = 0 . 7 4 7 4 0     | R | = 2 . 2 9 2 3 9     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
       1 9     p = 2 5 0 2 6 1 8 1                 D 5     g% = 3 6 . 1 5 9 4 7 6 9 1     d i g i t s = 7 5 3 3 6 3 2 
 
               s c o r e = 0 . 7 4 7 3 6     | R | = 2 . 2 9 2 2 9     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
       2 0     p = 2 5 0 2 7 6 2 7                 D 5     g% = 3 6 . 1 5 9 5 9 6 9 7     d i g i t s = 7 5 3 4 0 6 7 
 
               s c o r e = 0 . 7 4 7 2 2     | R | = 2 . 2 9 1 8 5     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
       2 1     p = 2 5 0 3 0 5 1 9                 D 5     g% = 3 6 . 1 5 9 8 3 7 0 9     d i g i t s = 7 5 3 4 9 3 8 
 
               s c o r e = 0 . 7 4 6 9 3     | R | = 2 . 2 9 0 9 8     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
       2 2     p = 2 5 0 3 2 8 8 1                 D 5     g% = 3 6 . 1 6 0 0 3 3 1 8     d i g i t s = 7 5 3 5 6 4 9 
 
               s c o r e = 0 . 7 4 6 6 9     | R | = 2 . 2 9 0 2 7     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
       2 3     p = 2 5 0 3 2 9 2 9                 D 5     g% = 3 6 . 1 6 0 0 3 7 1 6     d i g i t s = 7 5 3 5 6 6 3 
 
               s c o r e = 0 . 7 4 6 6 9     | R | = 2 . 2 9 0 2 6     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
       2 4     p = 2 5 0 3 5 5 8 1                 D 5     g% = 3 6 . 1 6 0 2 5 7 3 0     d i g i t s = 7 5 3 6 4 6 1 
 
               s c o r e = 0 . 7 4 6 4 2     | R | = 2 . 2 8 9 4 6     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
       2 5     p = 2 5 0 3 5 6 7 7                 D 5     g% = 3 6 . 1 6 0 2 6 5 2 7     d i g i t s = 7 5 3 6 4 9 0 
 
               s c o r e = 0 . 7 4 6 4 1     | R | = 2 . 2 8 9 4 3     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
       2 6     p = 2 5 0 3 7 5 5 7                 D 5     g% = 3 6 . 1 6 0 4 2 1 3 2     d i g i t s = 7 5 3 7 0 5 6 
 
               s c o r e = 0 . 7 4 6 2 2     | R | = 2 . 2 8 8 8 6     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
       2 7     p = 2 5 0 3 9 5 8 3                 D 5     g% = 3 6 . 1 6 0 5 8 9 4 6     d i g i t s = 7 5 3 7 6 6 6 
 
               s c o r e = 0 . 7 4 6 0 2     | R | = 2 . 2 8 8 2 5     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
       2 8     p = 2 5 0 4 0 0 1 7                 D 5     g% = 3 6 . 1 6 0 6 2 5 4 8     d i g i t s = 7 5 3 7 7 9 7 
 
               s c o r e = 0 . 7 4 5 9 8     | R | = 2 . 2 8 8 1 2     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
       2 9     p = 2 5 0 4 0 9 3 3                 D 5     g% = 3 6 . 1 6 0 7 0 1 5 0     d i g i t s = 7 5 3 8 0 7 2 
 
               s c o r e = 0 . 7 4 5 8 8     | R | = 2 . 2 8 7 8 4     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 2 s ) 
 
       3 0     p = 2 5 0 4 2 6 2 1                 D 5     g% = 3 6 . 1 6 0 8 4 1 5 8     d i g i t s = 7 5 3 8 5 8 1 
 
               s c o r e = 0 . 7 4 5 7 1     | R | = 2 . 2 8 7 3 3     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 2 . 0     ( 0 . 0 3 s ) 
 
 
 
 S a v e d :   m e r s e n n e _ s i e v e _ c a n d i d a t e s . t x t 
 
 
 
 = = =   C O N F I R M E D   C O M P O S I T E S   ( f a c t o r   f o u n d )   = = = 
 
     p = 2 5 0 0 3 0 5 7                 C O M P O S I T E :   4 2 2 4 6 6 6 5 2 9 0 6 3   %   ( 2 ^ p - 1 ) / 4 2 2 4 6 6 6 5 2 9 0 6 3   
 
     p = 2 5 0 0 4 1 1 7                 C O M P O S I T E :   1 6 0 3 7 6 4 0 6 4 3 9   %   ( 2 ^ p - 1 ) / 1 6 0 3 7 6 4 0 6 4 3 9     
 
     p = 2 5 0 0 6 5 7 3                 C O M P O S I T E :   4 0 0 1 0 5 1 6 9   %   ( 2 ^ p - 1 ) / 4 0 0 1 0 5 1 6 9           
 
     p = 2 5 0 0 7 9 2 1                 C O M P O S I T E :   8 0 0 2 5 3 4 7 3   %   ( 2 ^ p - 1 ) / 8 0 0 2 5 3 4 7 3           
 
     p = 2 5 0 1 0 2 3 3                 C O M P O S I T E :   2 3 5 5 9 6 3 9 4 8 7   %   ( 2 ^ p - 1 ) / 2 3 5 5 9 6 3 9 4 8 7       
 
     p = 2 5 0 1 6 3 9 9                 C O M P O S I T E :   5 0 0 3 2 7 9 9   %   ( 2 ^ p - 1 ) / 5 0 0 3 2 7 9 9             
 
     p = 2 5 0 1 8 6 6 3                 C O M P O S I T E :   1 5 6 1 1 6 4 5 7 1 3   %   ( 2 ^ p - 1 ) / 1 5 6 1 1 6 4 5 7 1 3       
 
     p = 2 5 0 2 0 1 5 7                 C O M P O S I T E :   3 5 8 1 2 3 5 1 5 2 0 3 9   %   ( 2 ^ p - 1 ) / 3 5 8 1 2 3 5 1 5 2 0 3 9   
 
     p = 2 5 0 2 6 3 7 3                 C O M P O S I T E :   1 6 1 5 5 0 2 4 2 9 8 9 7   %   ( 2 ^ p - 1 ) / 1 6 1 5 5 0 2 4 2 9 8 9 7   
 
     p = 2 5 0 3 0 7 1 1                 C O M P O S I T E :   2 3 2 7 8 5 6 1 2 3 1   %   ( 2 ^ p - 1 ) / 2 3 2 7 8 5 6 1 2 3 1       
 
 