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Old 2018-01-01, 17:39   #1
pinhodecarlos
 
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"Carlos Pinho"
Oct 2011
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Default Largest k*2^n-1 Primes Found In 2017

Here is the list of 100 largest "Riesel" primes (k*2^n-1, k>1) found in 2017.

Meaning of rank marks:
r1, rank on this list
r2, rank on the list of all known primes (as of January 1, 2018 at 1730 GMT)

Code:
----------------------------------------------------------------------
 r1     r2    description                        digits     who
----------------------------------------------------------------------
  1     29    273809*2^8932416-1		2688931    L1056
  2     35    737*2^7269322-1                   2188287    L4665
  3     70    5*2^5429494-1                     1634442    L3345
  4     72    1349*2^5385004-1                  1621051    L1828
  5    111    49*2^4365175-1                    1314051    L1959
  6    112    49*2^4360869-1                    1312755    L1959
  7    126    1031*2^4054974-1                  1220672    L1828
  8    189    1393*2^3525571-1                  1061306    L1828
  9    207    1061*2^3471354-1                  1044985    L1828
 10    243    342924651*2^3394939-1             1021988    L4166
 11    262    61*2^3366033-1                    1013279    L4405
 12    319    2017*2^3292325-1                   991092    L3345
 13    345    99*2^3102401-1                     933918    L1862
 14    406    45*2^2958002-1                     890449    L1862
 15    416    61*2^2936967-1                     884117    L2484
 16    431    99*2^2899303-1                     872780    L1862
 17    470    1337*2^2785444-1                   838506    L4518
 18    471    600921*2^2776014-1                 835670    g337
 19    513    4189*2^2666639-1                   802742    L1959
 20    555    229*2^2581111-1                    776995    L1862
 21    611    213*2^2493004-1                    750472    L1863
 22    647    12587*2^2462524-1                  741298    L2012
 23    687    4075*2^2417579-1                   727768    L1959
 24    716    1485*2^2386037-1                   718272    L1134
 25    725    1981*2^2375591-1                   715128    L1134
 26    764    335*2^2338972-1                    704104    L2235
 27    766    339*2^2336421-1                    703336    L2519
 28    773    213*2^2328530-1                    700960    L1863
 29    792    345*2^2313720-1                    696502    L2017
 30    824    213*2^2277870-1                    685710    L1863
 31    867    347*2^2245598-1                    675995    L2519
 32    966    4165*2^2171145-1                   653584    L1959
 33   1059    2503*2^2094587-1                   630537    L4113
 34   1109    213*2^2064426-1                    621457    L1863
 35   1145    4175*2^2032552-1                   611863    L1959
 36   1148    4157*2^2029894-1                   611063    L1959
 37   1154    4185*2^2026400-1                   610011    L1959
 38   1168    4101*2^2018133-1                   607523    L1959
 39   1169    4081*2^2015959-1                   606868    L1959
 40   1170    4191*2^2015150-1                   606625    L1959
 41   1231    4125*2^1984855-1                   597505    L1959
 42   1243    19920911*2^1974666-1               594441    L806
 43   1248    4197*2^1970430-1                   593163    L1959
 44   1567    1965*2^1803256-1                   542838    L4113
 45   1582    1965*2^1797877-1                   541219    L4113
 46   1589    10041*2^1795990-1                  540651    p168
 47   1797    1967*2^1710052-1                   514781    L4113
 48   1948    19920911*2^1648678-1               496309    L806
 49   1967    2715*2^1640137-1                   493734    L2484
 50   1996    2715*2^1629931-1                   490662    L2484
 51   2222    2955*2^1582609-1                   476417    L3887
 52   2270    2355*2^1571668-1                   473123    L2484
 53   2298    2925*2^1564031-1                   470824    L2484
 54   2326    3423*2^1555994-1                   468405    L860
 55   2329    3615*2^1555289-1                   468193    L860
 56   2333    3615*2^1554565-1                   467975    L860
 57   2373    3555*2^1542812-1                   464437    L860
 58   2438    8515*2^1525105-1                   459107    L1884
 59   2439    8515*2^1524873-1                   459037    L1884
 60   2461    541*2^1519465-1                    457408    L3844
 61   2469    2295*2^1517247-1                   456741    L2484
 62   2475    449*2^1516108-1                    456397    L3844
 63   2519    465*2^1504138-1                    452794    L3844
 64   2524    7863*2^1502299-1                   452241    L860
 65   2529    551*2^1501694-1                    452058    L3844
 66   2544    7473*2^1497216-1                   450711    L860
 67   2545    2145*2^1497137-1                   450687    L1863
 68   2557    2445*2^1495063-1                   450063    L2484
 69   2561    595*2^1494593-1                    449921    L2257
 70   2575    6825*2^1492542-1                   449304    L860
 71   2584    683*2^1491446-1                    448973    L2257
 72   2590    477*2^1489922-1                    448514    L1978
 73   2594    527*2^1489120-1                    448273    L2257
 74   2612    801*2^1486133-1                    447374    L2257
 75   2615    829*2^1484633-1                    446922    L2257
 76   2618    567*2^1484069-1                    446753    L1978
 77   2624    108045*2^1482857-1                 446390    L466
 78   2627    627*2^1482485-1                    446276    L1819
 79   2634    895*2^1480783-1                    445764    L1819
 80   2636    923*2^1480444-1                    445662    L2017
 81   2641    559*2^1478821-1                    445173    L2257
 82   2643    545*2^1478786-1                    445162    L2257
 83   2649    2547*2^1477754-1                   444852    L2484
 84   2653    867*2^1477169-1                    444676    L2017
 85   2654    675*2^1476887-1                    444591    L1819
 86   2679    741*2^1472086-1                    443145    L2257
 87   2680    7383*2^1472071-1                   443142    L860
 88   2690    10005*2^1469358-1                  442325    L4405
 89   2692    7917*2^1468572-1                   442089    L860
 90   2694    527*2^1468300-1                    442006    L3844
 91   2695    759*2^1468175-1                    441968    L2519
 92   2704    7125*2^1466093-1                   441342    L860
 93   2712    475*2^1464057-1                    440728    L3055
 94   2714    955*2^1463821-1                    440658    L2257
 95   2753    765*2^1460683-1                    439713    L2519
 96   2775    591*2^1458622-1                    439092    L3844
 97   2801    489*2^1456683-1                    438508    L3055
 98   2802    413*2^1456498-1                    438453    L3844
 99   2835    843*2^1453392-1                    437518    L2257
100   2847    513*2^1452354-1                    437205    L3844
---------------------------------------------------------------------
The list of 100 largest Riesel primes found in 2017 can be found
http://www.mersenneforum.org/showthread.php?t=21885

Last fiddled with by Thomas11 on 2018-01-01 at 18:11
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Old 2018-01-01, 17:44   #2
pinhodecarlos
 
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"Carlos Pinho"
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Sorry about the table format but when I edit it it shows me a clean table, after saving it it looks messy.
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Old 2018-01-01, 18:14   #3
Thomas11
 
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I adjusted the formatting of the table...
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Old 2018-01-01, 18:19   #4
pinhodecarlos
 
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Quote:
Originally Posted by Thomas11 View Post
I adjusted the formatting of the table...

Thank you.
Did you do it manually or is there a format code for it?
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Old 2018-01-01, 19:18   #5
paulunderwood
 
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You are missing a prime, the one with k=1
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Old 2018-01-01, 20:13   #6
pinhodecarlos
 
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Quote:
Originally Posted by paulunderwood View Post
You are missing a prime, the one with k=1
Not for k>1.

Last fiddled with by pinhodecarlos on 2018-01-01 at 20:35
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Old 2018-01-02, 05:11   #7
Kosmaj
 
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Hi Carlos and Thomas,

Thanks for a nice list.
And Happy New Year to everyone!
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Old 2018-01-02, 05:37   #8
George M
 
Dec 2017

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Post I believe these primes are called “Proth Primes”

Doing a little bit of research, these primes are called “Proth Primes”. We also have the Prime Gap Equation which when writing in TEX, I accidentally forgot to add 2 to the RHS. Here is the clean version.

p_{n+1} \ = \ \{2 \ + \ \sum_{k = 1}^n(p_{k + 1} \ - \ p_k) \ : \ p_m \ = \ m^{th} \ prime \ number\}

I mentioned this equation on three or four other threads I believe (Conjectures R Us, Prime Gap News, Predict M50/M51, etc) for I was trying to find a proof. Does anyone have a proof of this equation?

Last fiddled with by George M on 2018-01-02 at 05:38
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Old 2018-12-24, 09:08   #9
pinhodecarlos
 
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Hi RPS friends,

Someone will have to make this year’s list since I won’t be available to do it.
Thank you in advance,

Carlos
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Old 2018-12-26, 02:50   #10
Citrix
 
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You can use the search function on the website. Includes some primes in 2017 - as I used 365 days from today as the search option.

Code:
-----  -------------------------------- ------- ----- ---- --------------
 rank           description              digits  who year comment
-----  -------------------------------- ------- ----- ---- --------------
   18  8508301*2^17016603-1             5122515 L4784 2018 Woodall (**)
   56  127*2^6836153-1                  2057890 L1862 2018 
   96  43*2^5408183-1                   1628027 L1884 2018 
  125  1229*2^4703492-1                 1415896 L1828 2018 
  129  79*2^4658115-1                   1402235 L1884 2018 
  142  13*2^4333087-1                   1304391 L1862 2018 
  149  1091*2^4215518-1                 1269001 L1828 2018 
  168  1199*2^3889576-1                 1170883 L1828 2018 
  189  119*2^3698412-1                  1113336 L2484 2018 
  197  215*2^3628962-1                  1092429 L2484 2018 
  211  119*2^3571416-1                  1075106 L2484 2018 
  217  265*2^3564373-1                  1072986 L2484 2018 
  223  1103*2^3558176-1                 1071121 L1828 2018 
  224  1379*2^3557072-1                 1070789 L1828 2018 
  229  1199*2^3548380-1                 1068172 L1828 2018 
  443  600921*2^3219922-1                969299  g337 2018 
  450  600921*2^3173683-1                955380  g337 2018 
  468  45*2^3094632-1                    931579 L1862 2018 
  480  271*2^3079189-1                   926931 L2484 2018 
  556  169*2^2917805-1                   878350 L2484 2018 
  580  241*2^2857313-1                   860140 L2484 2018 
  613  215*2^2751022-1                   828143 L2484 2018 
  620  1981*2^2728877-1                  821478 L1134 2018 
  761  303*2^2562423-1                   771369 L2017 2018 
  776  311*2^2544778-1                   766058 L2017 2018 
  794  241*2^2522801-1                   759442 L2484 2018 
  797  199*2^2518871-1                   758259 L2484 2018 
  815  319*2^2498685-1                   752182 L2017 2018 
  816  321*2^2496594-1                   751553 L2235 2018 
  843  325*2^2473267-1                   744531 L2017 2018 
  849  119*2^2468556-1                   743112 L2484 2018 
  895  239*2^2421404-1                   728918 L2484 2018 
  899  303*2^2417452-1                   727729 L2235 2018 
  902  333*2^2412735-1                   726309 L2017 2018 
  903  83*2^2411962-1                    726075 L1959 2018 
  937  321*2^2378535-1                   716013 L2017 2018 
  943  97*2^2374485-1                    714794 L2484 2018 
  961  305*2^2358854-1                   710089 L2017 2018 
  983  335*2^2338972-1                   704104 L2235 2017 
  987  105*2^2334755-1                   702834 L1959 2018 
 1068  265*2^2258071-1                   679750 L2484 2018 
 1125  271*2^2223601-1                   669374 L2484 2018 
 1168  169*2^2193049-1                   660176 L2484 2018 
 1250  241*2^2135279-1                   642786 L2484 2018 
 1254  215*2^2131988-1                   641795 L2484 2018 
 1306  217*2^2092673-1                   629960 L2484 2018 
 1372  265*2^2051155-1                   617462 L2484 2018 
 1689  2655*2^1879275-1                  565722 L2484 2018 
 1736  2655*2^1859692-1                  559827 L1862 2018 
 1840  10007*2^1811598-1                 545350 L1751 2018 
 1861  2415*2^1801615-1                  542344 L2484 2018 
 1970  2895*2^1762011-1                  530422 L2484 2018 
 1982  2565*2^1758906-1                  529487 L2484 2018 
 2010  2955*2^1748957-1                  526492 L2484 2018 
 2096  57257*2^1719090-1                 517503 L4812 2018 
 2299  2925*2^1657921-1                  499088 L2484 2018 
 2378  2325*2^1646536-1                  495661 L2484 2018 
 2412  2715*2^1640137-1                  493734 L2484 2017 
 2481  2715*2^1629931-1                  490662 L2484 2017 
 2594  10005*2^1606698-1                 483669 L4405 2018 
 2606  320607*2^1604657-1                483056  g337 2018 
 2726  551*2^1583718-1                   476750 L3994 2018 
 2730  433*2^1583059-1                   476551 L3994 2018 
 2737  471*2^1582593-1                   476411 L3994 2018 
 2754  449*2^1579160-1                   475378 L3994 2018 
 2771  427*2^1577169-1                   474778 L3994 2018 
 2782  557*2^1575504-1                   474277 L3994 2018 
 2791  557*2^1571700-1                   473132 L3994 2018 
 2825  597*2^1563213-1                   470577 L2519 2018 
 2952  939*2^1532143-1                   461224 L2257 2018 
 2953  815*2^1531386-1                   460997 L2257 2018 
 2961  951*2^1530151-1                   460625 L2257 2018 
 2968  633*2^1529603-1                   460460 L2257 2018 
 2989  621*2^1524287-1                   458859 L2519 2018 
 2996  889*2^1522531-1                   458331 L2257 2018 
 3016  741*2^1518755-1                   457194 L2017 2018 
 3044  689*2^1512316-1                   455256 L2257 2018 
 3046  871*2^1511925-1                   455138 L2257 2018 
 3053  607*2^1510953-1                   454845 L1978 2018 
 3058  625*2^1509873-1                   454520 L2257 2018 
 3124  825*2^1504415-1                   452877 L1817 2018 
 3145  691*2^1503141-1                   452494 L2257 2018 
 3179  691*2^1500869-1                   451810 L1819 2018 
 3207  837*2^1498329-1                   451045 L1819 2018 
 3210  855*2^1498084-1                   450972 L1819 2018 
 3259  703*2^1494427-1                   449871 L2257 2018 
 3261  745*2^1494273-1                   449824 L1819 2018 
 3270  975*2^1493869-1                   449703 L2257 2018 
 3516  405405*2^1476144-1                444370  L466 2018 
 3825  320607*2^1452298-1                437191  g337 2018 
 4812  78557*2^1383002-1                 416330  p401 2018 
55326  13375563435*2^137137-1             41293  p364 2018 
          Sophie Germain (2p+1)
55327  13375563435*2^137136-1             41293  p364 2018 Sophie Germain (p)
55784  10429091973*2^135136-1             40691  p364 2018 
          Sophie Germain (2p+1)
55785  10429091973*2^135135-1             40690  p364 2018 Sophie Germain (p)
56073  73378515705*2^133148-1             40093  L167 2018 
          Sophie Germain (2p+1)
56074  73378515705*2^133147-1             40093  L167 2018 Sophie Germain (p)
73289  14059969053*2^36672-1              11050  p364 2018 Triplet (2)
85405  101406820312263*2^12042-1           3640  p364 2018 Quadruplet (1)

Last fiddled with by Citrix on 2018-12-26 at 02:57 Reason: *2^%-1$
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