Largest k*2^n-1 Primes Found In 2020

andyhedges · 2021-01-01, 22:01

Here is the list of 45 50 largest "Riesel" primes (k*2^n-1, k>1) found in 2020.
(Again less than 100 Riesel primes have been submitted to the Top5000 list in 2020.)

Meaning of rank marks:
r1, rank on this list
r2, rank on the list of all known primes (as of January 1, 2021 at 22:00 GMT)

Code:

---------------------------------------------------
r1    r2 description               digits  who  
---------------------------------------------------
 1    36 69*2^11718455-1           3527609 L4965
 2    37 69*2^11604348-1           3493259 L4965
 3    44 146561*2^11280802-1       3395865 L5181
 4   101 69*2^6838971-1            2058738 L5037
 5   106 283*2^6804731-1           2048431 L2484
 6   109 9995*2^6711008-1          2020219 L4965
 7   115 69*2^6639971-1            1998833 L5037
 8   195 25*2^5152151-1            1550954 L1884
 9   248 195*2^4373994-1           1316706 L5175
10   577 3329*2^3388472-1          1020036 L4841
11   796 3659465685*2^3321910-1    1000005 L4960
12   797 3652932033*2^3321910-1    1000005 L4960
13   798 3603204333*2^3321910-1    1000005 L4960
14   799 3543733545*2^3321910-1    1000005 L4960
15   800 3191900133*2^3321910-1    1000005 L4960
16   801 3174957723*2^3321910-1    1000005 L4960
17   805 2611553775*2^3321910-1    1000004 L4960
18   935 57*2^3093440-1             931220 L2484
19   947 65*2^3080952-1             927461 L2484
20   970 111*2^3060238-1            921226 L2484
21   983 99*2^3029959-1             912111 L1862
22   985 99*2^3026660-1             911118 L1862
23  1239 335*2^2708958-1            815481 L2235
24  1270 1455*2^2683953-1           807954 L1134
25  1538 1425*2^2435607-1           733194 L1134
26  1545 233*2^2426512-1            730456 L2484
27  1722 1001*2^2289438-1           689193 L4518
28  2012 1425*2^2101260-1           632546 L1134
29  2013 1001*2^2101062-1           632486 L4518
30  2020 695265*2^2097153-1         631312 L466 
31  2151 273*2^2024810-1            609531 L5118
32  2755 1471*2^1772755-1           533656 L1830
33  2973 999*2^1733065-1            521708 L4518
34  3521 999*2^1683539-1            506799 L4518
35  4097 471*2^1604233-1            482925 L5184
36  4233 595*2^1594415-1            479970 L3994
37  4436 10009*2^1580131-1          475671 L4405
38  4533 10005*2^1573410-1          473648 L4405
39  4607 717*2^1567550-1            471883 L1817
40  4635 805*2^1565131-1            471155 L1817
41  4657 685*2^1563423-1            470641 L1817
42  8561 9422094211005*2^1290000-1  388342 L3494
43  8563 4966510140375*2^1290000-1  388342 L3573
44  8564 4953427788675*2^1290000-1  388342 L3573
45 50254 1068669447*2^211089-1       63554 L4166
46 50255 1068669447*2^211088-1       63553 L4166
47 54174 191547657*2^173372-1        52199 L5116
48 67060 1128330746865*2^66441-1     20013 p158 
49 67061 1128330746865*2^66440-1     20013 p158 
50 67063 1128330746865*2^66439-1     20013 p158

The list of 78 largest Riesel primes found in 2019 can be found here

Batalov · 2021-01-01, 22:12

I am finding five more, 50 in total:

Code:

-----  -------------------------------- ------- ----- ---- --------------
 rank           description              digits  who year comment
-----  -------------------------------- ------- ----- ---- --------------
   36  69*2^11718455-1                  3527609 L4965 2020 
   37  69*2^11604348-1                  3493259 L4965 2020 
   44  146561*2^11280802-1              3395865 L5181 2020 (**)
  101  69*2^6838971-1                   2058738 L5037 2020 
  106  283*2^6804731-1                  2048431 L2484 2020 
  109  9995*2^6711008-1                 2020219 L4965 2020  <<<---
  115  69*2^6639971-1                   1998833 L5037 2020 
  195  25*2^5152151-1                   1550954 L1884 2020 
  248  195*2^4373994-1                  1316706 L5175 2020 
  577  3329*2^3388472-1                 1020036 L4841 2020 
  796  3659465685*2^3321910-1           1000005 L4960 2020 
  797  3652932033*2^3321910-1           1000005 L4960 2020 
  798  3603204333*2^3321910-1           1000005 L4960 2020 
  799  3543733545*2^3321910-1           1000005 L4960 2020 
  800  3191900133*2^3321910-1           1000005 L4960 2020 
  801  3174957723*2^3321910-1           1000005 L4960 2020 
  805  2611553775*2^3321910-1           1000004 L4960 2020 
  935  57*2^3093440-1                    931220 L2484 2020 
  947  65*2^3080952-1                    927461 L2484 2020 
  970  111*2^3060238-1                   921226 L2484 2020 
  983  99*2^3029959-1                    912111 L1862 2020 
  985  99*2^3026660-1                    911118 L1862 2020 
 1239  335*2^2708958-1                   815481 L2235 2020 
 1270  1455*2^2683953-1                  807954 L1134 2020 
 1538  1425*2^2435607-1                  733194 L1134 2020 
 1545  233*2^2426512-1                   730456 L2484 2020 
 1722  1001*2^2289438-1                  689193 L4518 2020 
 2012  1425*2^2101260-1                  632546 L1134 2020 
 2013  1001*2^2101062-1                  632486 L4518 2020 
 2020  695265*2^2097153-1                631312  L466 2020 
 2151  273*2^2024810-1                   609531 L5118 2020 
 2755  1471*2^1772755-1                  533656 L1830 2020 
 2973  999*2^1733065-1                   521708 L4518 2020 
 3521  999*2^1683539-1                   506799 L4518 2020 
 4097  471*2^1604233-1                   482925 L5184 2020 
 4233  595*2^1594415-1                   479970 L3994 2020 
 4436  10009*2^1580131-1                 475671 L4405 2020 
 4533  10005*2^1573410-1                 473648 L4405 2020 
 4607  717*2^1567550-1                   471883 L1817 2020 
 4635  805*2^1565131-1                   471155 L1817 2020 
 4657  685*2^1563423-1                   470641 L1817 2020 
 8561  9422094211005*2^1290000-1         388342 L3494 2020 Arithmetic progression (3,d=2227792035315*2^1290001)
 8563  4966510140375*2^1290000-1         388342 L3573 2020 Arithmetic progression (2,d=2227792035315*2^1290001)
 8564  4953427788675*2^1290000-1         388342 L3573 2020 Arithmetic progression (2,d=3555*2^1542812-4953427788675*2^1290000)
50254  1068669447*2^211089-1              63554 L4166 2020 Sophie Germain (2p+1)
50255  1068669447*2^211088-1              63553 L4166 2020 Sophie Germain (p)
54174  191547657*2^173372-1               52199 L5116 2020 Twin (p)
67060  1128330746865*2^66441-1            20013  p158 2020 Cunningham chain (4p+3)
67061  1128330746865*2^66440-1            20013  p158 2020 Cunningham chain (2p+1)
67063  1128330746865*2^66439-1            20013  p158 2020 Cunningham chain (p)
-----  -------------------------------- ------- ----- ---- --------------

andyhedges · 2021-01-01, 23:32

This is strange. I'm getting the data from here:

https://primes.utm.edu/primes/lists/all.txt

As an example I can't see 9995*2^6711008-1 in this list linked above.

paulunderwood · 2021-01-01, 23:40

It is in progress of being verified according to the status page. Most likely it will appear when the search page is used.

Batalov · 2021-01-01, 23:45

Two weaknesses of using that file: 1) you won't find entries in progress, 2) you won't find entries that legitimately entered the database in 2020 but by the end of the year left the list.
...but they were found in 2020, so they belong on the list.

It is (fairly) easy though.
You use the search page, use "all" option, and use age: max=366, and search limit "500". And finally, the search pattern: ^[[:digit:]]{1,}*2^[[:digit:]]{1,}-1$
And then you lightly edit, if necessary.

(For example next year, if you use "366" days, you might miss a very early 1/1/2020 entry, but if you use "367" you will catch that "between years" Ryan's submission, again. 2020 is leap, so 366 will becomes 367

)

andyhedges · 2021-01-02, 00:09

Ah I see, thanks for explaining. Here's a new version. If a mod would like to delete my post and repost a neater copy that would be great :)

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2021-01-01, 23:32	#3
andyhedges Mar 2016 2² Posts	This is strange. I'm getting the data from here: https://primes.utm.edu/primes/lists/all.txt As an example I can't see 9995*2^6711008-1 in this list linked above.

2021-01-01, 23:40	#4
paulunderwood Sep 2002 Database er0rr 2×3×691 Posts	It is in progress of being verified according to the status page. Most likely it will appear when the search page is used.

2021-01-01, 23:45	#5
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2³×1,229 Posts	Two weaknesses of using that file: 1) you won't find entries in progress, 2) you won't find entries that legitimately entered the database in 2020 but by the end of the year left the list. ...but they were found in 2020, so they belong on the list. It is (fairly) easy though. You use the search page, use "all" option, and use age: max=366, and search limit "500". And finally, the search pattern: ^[[:digit:]]{1,}*2^[[:digit:]]{1,}-1$ And then you lightly edit, if necessary. (For example next year, if you use "366" days, you might miss a very early 1/1/2020 entry, but if you use "367" you will catch that "between years" Ryan's submission, again. 2020 is leap, so 366 will becomes 367 )

2021-01-02, 00:09	#6
andyhedges Mar 2016 2² Posts	Ah I see, thanks for explaining. Here's a new version. If a mod would like to delete my post and repost a neater copy that would be great :)