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-   -   Largest k*2^n-1 Primes Found In 2017 (https://www.mersenneforum.org/showthread.php?t=22867)

pinhodecarlos 2018-01-01 17:39

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
---------------------------------------------------------------------
[/CODE]The list of 100 largest Riesel primes found in 2017 can be found
[URL]http://www.mersenneforum.org/showthread.php?t=21885[/URL]

pinhodecarlos 2018-01-01 17:44

Sorry about the table format but when I edit it it shows me a clean table, after saving it it looks messy.

Thomas11 2018-01-01 18:14

I adjusted the formatting of the table...

pinhodecarlos 2018-01-01 18:19

[QUOTE=Thomas11;475861]I adjusted the formatting of the table...[/QUOTE]


Thank you.
Did you do it manually or is there a format code for it?

paulunderwood 2018-01-01 19:18

You are missing a prime, the one with k=1 :wink:

pinhodecarlos 2018-01-01 20:13

[QUOTE=paulunderwood;475867]You are missing a prime, the one with k=1 :wink:[/QUOTE]

Not for k>1.

Kosmaj 2018-01-02 05:11

Hi Carlos and Thomas,

Thanks for a nice list.
And Happy New Year to everyone!

George M 2018-01-02 05:37

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.

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

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?

pinhodecarlos 2018-12-24 09:08

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

Citrix 2018-12-26 02:50

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)
[/code]


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