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 = = =   M E R S E N N E   C A N D I D A T E   S I E V E   = = = 
 
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 
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 = = =   S I E V E   R E S U L T S   = = = 
 
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 
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 
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 
 S u r v i v e d   ( n o   f a c t o r   t o   2 ^ 4 0 . 0 ) :   1 1 1 
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 = = =   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 0 . 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 2 5 0 2 2 0 9                 D 4     g% = 3 5 . 9 3 8 5 5 7 4 9     d i g i t s = 6 7 7 3 8 4 0 
 
               s c o r e = 0 . 7 4 9 8 3     | R | = 2 . 5 3 1 9 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 0 . 0     ( 0 . 0 1 s ) 
 
         2     p = 2 2 5 0 2 5 7 3                 D 4     g% = 3 5 . 9 3 8 5 9 1 1 1     d i g i t s = 6 7 7 3 9 5 0 
 
               s c o r e = 0 . 7 4 9 8 1     | R | = 2 . 5 3 1 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 0 . 0     ( 0 . 0 1 s ) 
 
         3     p = 2 2 5 0 2 6 7 7                 D 4     g% = 3 5 . 9 3 8 6 0 0 7 1     d i g i t s = 6 7 7 3 9 8 1 
 
               s c o r e = 0 . 7 4 9 8 0     | R | = 2 . 5 3 1 9 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 0 . 0     ( 0 . 0 1 s ) 
 
         4     p = 2 2 5 0 2 7 2 9                 D 4     g% = 3 5 . 9 3 8 6 0 5 5 1     d i g i t s = 6 7 7 3 9 9 7 
 
               s c o r e = 0 . 7 4 9 8 0     | R | = 2 . 5 3 2 0 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 0 . 0     ( 0 . 0 1 s ) 
 
         5     p = 2 2 5 0 3 4 5 7                 D 4     g% = 3 5 . 9 3 8 6 7 2 7 4     d i g i t s = 6 7 7 4 2 1 6 
 
               s c o r e = 0 . 7 4 9 7 4     | R | = 2 . 5 3 2 1 1     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 0 . 0     ( 0 . 0 1 s ) 
 
         6     p = 2 2 5 0 3 7 6 9                 D 4     g% = 3 5 . 9 3 8 7 0 1 5 5     d i g i t s = 6 7 7 4 3 1 0 
 
               s c o r e = 0 . 7 4 9 7 2     | R | = 2 . 5 3 2 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 0 . 0     ( 0 . 0 1 s ) 
 
         7     p = 2 2 5 0 4 8 6 1                 D 4     g% = 3 5 . 9 3 8 8 0 2 3 9     d i g i t s = 6 7 7 4 6 3 9 
 
               s c o r e = 0 . 7 4 9 6 4     | R | = 2 . 5 3 2 3 1     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 0 . 0     ( 0 . 0 1 s ) 
 
         8     p = 2 2 5 0 5 3 8 1                 D 4     g% = 3 5 . 9 3 8 8 5 0 4 1     d i g i t s = 6 7 7 4 7 9 5 
 
               s c o r e = 0 . 7 4 9 6 0     | R | = 2 . 5 3 2 3 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 0 . 0     ( 0 . 0 1 s ) 
 
         9     p = 2 2 5 0 6 1 0 9                 D 4     g% = 3 5 . 9 3 8 9 1 7 6 3     d i g i t s = 6 7 7 5 0 1 4 
 
               s c o r e = 0 . 7 4 9 5 4     | R | = 2 . 5 3 2 4 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 0 . 0     ( 0 . 0 1 s ) 
 
       1 0     p = 2 2 5 0 6 1 6 1                 D 4     g% = 3 5 . 9 3 8 9 2 2 4 3     d i g i t s = 6 7 7 5 0 3 0 
 
               s c o r e = 0 . 7 4 9 5 4     | R | = 2 . 5 3 2 4 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 0 . 0     ( 0 . 0 1 s ) 
 
       1 1     p = 2 2 5 0 6 7 3 3                 D 4     g% = 3 5 . 9 3 8 9 7 5 2 4     d i g i t s = 6 7 7 5 2 0 2 
 
               s c o r e = 0 . 7 4 9 5 0     | R | = 2 . 5 3 2 5 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 0 . 0     ( 0 . 0 1 s ) 
 
       1 2     p = 2 2 5 0 6 8 8 9                 D 4     g% = 3 5 . 9 3 8 9 8 9 6 5     d i g i t s = 6 7 7 5 2 4 9 
 
               s c o r e = 0 . 7 4 9 4 9     | R | = 2 . 5 3 2 5 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 0 . 0     ( 0 . 0 1 s ) 
 
       1 3     p = 2 2 5 0 7 2 5 3                 D 4     g% = 3 5 . 9 3 9 0 2 3 2 5     d i g i t s = 6 7 7 5 3 5 9 
 
               s c o r e = 0 . 7 4 9 4 6     | R | = 2 . 5 3 2 6 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 0 . 0     ( 0 . 0 1 s ) 
 
       1 4     p = 2 2 5 0 7 9 8 1                 D 4     g% = 3 5 . 9 3 9 0 9 0 4 7     d i g i t s = 6 7 7 5 5 7 8 
 
               s c o r e = 0 . 7 4 9 4 0     | R | = 2 . 5 3 2 7 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 0 . 0     ( 0 . 0 1 s ) 
 
       1 5     p = 2 2 5 0 8 1 3 7                 D 4     g% = 3 5 . 9 3 9 1 0 4 8 7     d i g i t s = 6 7 7 5 6 2 5 
 
               s c o r e = 0 . 7 4 9 3 9     | R | = 2 . 5 3 2 7 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 0 . 0     ( 0 . 0 1 s ) 
 
       1 6     p = 2 2 5 0 8 6 5 7                 D 4     g% = 3 5 . 9 3 9 1 5 2 8 8     d i g i t s = 6 7 7 5 7 8 1 
 
               s c o r e = 0 . 7 4 9 3 5     | R | = 2 . 5 3 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 0 . 0     ( 0 . 0 1 s ) 
 
       1 7     p = 2 2 5 0 9 0 7 3                 D 4     g% = 3 5 . 9 3 9 1 9 1 2 9     d i g i t s = 6 7 7 5 9 0 7 
 
               s c o r e = 0 . 7 4 9 3 2     | R | = 2 . 5 3 2 9 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 0 . 0     ( 0 . 0 1 s ) 
 
       1 8     p = 2 2 5 0 9 2 2 9                 D 4     g% = 3 5 . 9 3 9 2 0 5 6 9     d i g i t s = 6 7 7 5 9 5 4 
 
               s c o r e = 0 . 7 4 9 3 1     | R | = 2 . 5 3 2 9 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 0 . 0     ( 0 . 0 1 s ) 
 
       1 9     p = 2 2 5 0 9 4 3 7                 D 4     g% = 3 5 . 9 3 9 2 2 4 8 9     d i g i t s = 6 7 7 6 0 1 6 
 
               s c o r e = 0 . 7 4 9 3 0     | R | = 2 . 5 3 2 9 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 0 . 0     ( 0 . 0 1 s ) 
 
       2 0     p = 2 2 5 0 9 7 4 9                 D 4     g% = 3 5 . 9 3 9 2 5 3 7 0     d i g i t s = 6 7 7 6 1 1 0 
 
               s c o r e = 0 . 7 4 9 2 7     | R | = 2 . 5 3 3 0 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 0 . 0     ( 0 . 0 1 s ) 
 
       2 1     p = 2 2 5 1 0 5 2 9                 D 4     g% = 3 5 . 9 3 9 3 2 5 7 0     d i g i t s = 6 7 7 6 3 4 5 
 
               s c o r e = 0 . 7 4 9 2 1     | R | = 2 . 5 3 3 1 1     s t a t u s = S U R V I V E D                             s i e v e d _ t o = 2 ^ 4 0 . 0     ( 0 . 0 1 s ) 
 
       2 2     p = 2 2 5 1 0 8 4 1                 D 4     g% = 3 5 . 9 3 9 3 5 4 5 1     d i g i t s = 6 7 7 6 4 3 9 
 
               s c o r e = 0 . 7 4 9 1 9     | R | = 2 . 5 3 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 0 . 0     ( 0 . 0 1 s ) 
 
       2 3     p = 2 2 5 1 1 7 7 7                 D 4     g% = 3 5 . 9 3 9 4 4 0 9 1     d i g i t s = 6 7 7 6 7 2 1 
 
               s c o r e = 0 . 7 4 9 1 2     | R | = 2 . 5 3 3 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 0 . 0     ( 0 . 0 1 s ) 
 
       2 4     p = 2 2 5 1 2 5 5 7                 D 4     g% = 3 5 . 9 3 9 5 1 2 9 1     d i g i t s = 6 7 7 6 9 5 5 
 
               s c o r e = 0 . 7 4 9 0 6     | R | = 2 . 5 3 3 4 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 0 . 0     ( 0 . 0 1 s ) 
 
       2 5     p = 2 2 5 1 2 7 1 3                 D 4     g% = 3 5 . 9 3 9 5 2 7 3 1     d i g i t s = 6 7 7 7 0 0 2 
 
               s c o r e = 0 . 7 4 9 0 5     | R | = 2 . 5 3 3 4 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 0 . 0     ( 0 . 0 1 s ) 
 
       2 6     p = 2 2 5 1 2 8 6 9                 D 4     g% = 3 5 . 9 3 9 5 4 1 7 1     d i g i t s = 6 7 7 7 0 4 9 
 
               s c o r e = 0 . 7 4 9 0 4     | R | = 2 . 5 3 3 4 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 0 . 0     ( 0 . 0 1 s ) 
 
       2 7     p = 2 2 5 1 3 1 2 9                 D 4     g% = 3 5 . 9 3 9 5 6 5 7 1     d i g i t s = 6 7 7 7 1 2 8 
 
               s c o r e = 0 . 7 4 9 0 2     | R | = 2 . 5 3 3 4 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 0 . 0     ( 0 . 0 1 s ) 
 
       2 8     p = 2 2 5 1 3 5 9 7                 D 4     g% = 3 5 . 9 3 9 6 0 8 9 1     d i g i t s = 6 7 7 7 2 6 9 
 
               s c o r e = 0 . 7 4 8 9 9     | R | = 2 . 5 3 3 5 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 0 . 0     ( 0 . 0 1 s ) 
 
       2 9     p = 2 2 5 1 4 1 1 7                 D 4     g% = 3 5 . 9 3 9 6 5 6 9 1     d i g i t s = 6 7 7 7 4 2 5 
 
               s c o r e = 0 . 7 4 8 9 5     | R | = 2 . 5 3 3 6 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 0 . 0     ( 0 . 0 1 s ) 
 
       3 0     p = 2 2 5 1 4 5 3 3                 D 4     g% = 3 5 . 9 3 9 6 9 5 3 1     d i g i t s = 6 7 7 7 5 5 0 
 
               s c o r e = 0 . 7 4 8 9 2     | R | = 2 . 5 3 3 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 0 . 0     ( 0 . 0 1 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 2 5 0 4 0 8 1                 C O M P O S I T E :   1 3 5 0 2 4 4 8 6 0 1   %   ( 2 ^ p - 1 ) / 1 3 5 0 2 4 4 8 6 0 1       
 
     p = 2 2 5 0 4 3 9 3                 C O M P O S I T E :   6 7 5 1 3 1 7 9 1   %   ( 2 ^ p - 1 ) / 6 7 5 1 3 1 7 9 1           
 
     p = 2 2 5 0 6 5 7 7                 C O M P O S I T E :   3 7 7 1 6 5 2 1 7 3 6 7   %   ( 2 ^ p - 1 ) / 3 7 7 1 6 5 2 1 7 3 6 7     
 
     p = 2 2 5 0 6 6 2 9                 C O M P O S I T E :   1 8 0 0 5 3 0 3 3   %   ( 2 ^ p - 1 ) / 1 8 0 0 5 3 0 3 3           
 
     p = 2 2 5 0 7 3 5 7                 C O M P O S I T E :   2 8 0 3 0 6 6 2 4 0 7 9   %   ( 2 ^ p - 1 ) / 2 8 0 3 0 6 6 2 4 0 7 9     
 
     p = 2 2 5 1 0 2 1 7                 C O M P O S I T E :   4 7 8 5 6 7 2 1 3 4 3   %   ( 2 ^ p - 1 ) / 4 7 8 5 6 7 2 1 3 4 3       
 
     p = 2 2 5 1 1 1 0 1                 C O M P O S I T E :   3 6 0 1 7 7 6 1 7   %   ( 2 ^ p - 1 ) / 3 6 0 1 7 7 6 1 7           
 
     p = 2 2 5 1 2 6 6 1                 C O M P O S I T E :   3 2 8 8 6 4 9 5 1 8 8 9   %   ( 2 ^ p - 1 ) / 3 2 8 8 6 4 9 5 1 8 8 9     
 
     p = 2 2 5 1 4 3 7 7                 C O M P O S I T E :   2 6 2 9 6 7 9 2 3 3 7   %   ( 2 ^ p - 1 ) / 2 6 2 9 6 7 9 2 3 3 7       
 
     p = 2 2 5 1 8 8 5 1                 C O M P O S I T E :   1 8 0 1 5 0 8 0 9   %   ( 2 ^ p - 1 ) / 1 8 0 1 5 0 8 0 9           
 
 