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7/26/2019 MPQS With Three Large Primes, http://slidepdf.com/reader/full/mpqs-with-three-large-primes 1/15

MPQS With Three Large Primes,

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Page 1: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

http://slidepdf.com/reader/full/mpqs-with-three-large-primes 1/15

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Æ  

 

 

 

 

 

 

 

 

 

Æ  

   

 

 

 

 

 

Æ  

 

 

Page 2: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

http://slidepdf.com/reader/full/mpqs-with-three-large-primes 2/15

 

 

 

 

 

 

 

   

 

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Æ

 

 

 

 

 

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Page 3: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

http://slidepdf.com/reader/full/mpqs-with-three-large-primes 3/15

 

     

∈ 

   

     

   

   

     

   

 

       

 

 

 

 

       

 

 

≤ 

 

 

   

 

 

 

 

 

 

     

 

 

 

 

Æ

 

 

   

 

 

 

 

 

≤ 

 

 

   

 

 

 

   

 

 

   

 

 

   

 

 

 

 

 

       

 

 

             

   

 

 

 

             

 

Page 4: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

http://slidepdf.com/reader/full/mpqs-with-three-large-primes 4/15

 

 

 

 

 

                 

 

 

 

 

 

 

 

   

      

 

     

≤ 

 

 

           

 

   

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  Æ   

 

       

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Page 5: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

http://slidepdf.com/reader/full/mpqs-with-three-large-primes 5/15

 

   

 

     

     

            

 

 

 

 

 

 

     

 

 

       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Page 6: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

http://slidepdf.com/reader/full/mpqs-with-three-large-primes 6/15

 

 

 

 

 

 

 

 

 

 

∗     

 

 

 

    ×  

 

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Æ  

 

 

 

 

 

 

      

 

     

 

 

 

  

 

 

         

 

 

Page 7: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

http://slidepdf.com/reader/full/mpqs-with-three-large-primes 7/15

       

 

 

 

 

     

   

 

   

 

     

 

 

y = 2.7665x - 33.608

R2 = 0.9626

0

2

4

6

8

10

12

14

12.5 13 13.5 14 14.5 15 15.5 16 16.5

   

 

 

 

 

     

     

     

   

 

Page 8: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

http://slidepdf.com/reader/full/mpqs-with-three-large-primes 8/15

 

         

             

             

 

     

   

       

 

Æ

   

y = 2.078x - 23.921

R2 = 0.9997

0

2

4

6

8

10

12

12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17

   

             

 

   

 

 

 

       

 

     

      

 

     

 

Page 9: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

http://slidepdf.com/reader/full/mpqs-with-three-large-primes 9/15

                 

           

           

     

   

y = 3.4969x - 46.804

R2 = 0.9984

0

2

4

6

8

10

12

14

14 14.5 15 15.5 16 16.5

     

   

 

 

                 

     

 

     

   

     

             

      

 

   

 

 

Page 10: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

http://slidepdf.com/reader/full/mpqs-with-three-large-primes 10/15

y = 7.3207x - 107.95

R2 = 0.9646

0

2

4

6

8

10

12

14

16

18

14.9 15.1 15.3 15.5 15.7 15.9 16.1 16.3 16.5

   

 

 

     

 

 

 

   

     

 

 

 

 

 

   

 

Page 11: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

http://slidepdf.com/reader/full/mpqs-with-three-large-primes 11/15

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Page 12: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

http://slidepdf.com/reader/full/mpqs-with-three-large-primes 12/15

 

 

 

 

           

 

          −    

-0.5

0

0.5

1

1.5

2

2.5

3

14.9 15.1 15.3 15.5 15.7 15.9 16.1 16.3 16.5

      −          

 

 

 

     

 

 

 

   

 

 

 

 

 

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Page 14: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

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Page 15: MPQS With Three Large Primes,

7/26/2019 MPQS With Three Large Primes,

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