Updated: 2026-07-17

I am doing some independent LLR tests on
Proth numbers k*2^n+1 with n≥5,000,000
for k<300, it is a verification

(6-digit k search)
n=5000000, sieved up to [1716T],
  all k up to 5 digits done,
  6 digit k<105,000 ...

(5-digit k search)
n=5000001-5000009, sieved up to [100T]
  all k<10,000 done.
 n=5000001 [454T] k<26,000 ... ...
 n=5000002 [180T] k<15,000 ...
 n=5000003 [103T] k<13,000 ...
 n=5000004 [100T] k<13,000 ...
 n=5000005 [105T] k<13,000 ...
 n=5000006 [102T] k<12,000 ...
 n=5000007 [103T] k<12,000 ...
 n=5000008 [102T] k<13,000 ...
 n=5000009 [102T] k<10,000

(less than 4 digit search)
n=5000010-5000049, sieved up to [10T]
  all k<1,000 done

[all the results must be archived here]


nothing found yet

it is being more than 6 months

expectations

looking at the results from Caldwell's list, which we can assume it is complete up to 2 digits for n<6,000,000 5013361 131 (2024) 5019181 53 (2023) 5054502 5359 (2003 SB6) 5082306 3 (2009) 5642513 9 (2013) 5775996 7 (2012) we can expect 5100000 k 5010000 kk 5001000 kkk 10T 5000100 kkkk 100T 5000010 kkkkk 1000T 5000001 kkkkkk 10000T you know what I mean.
each ... is a running core, equivalent to 4 tests per day 8 cores of 3069 MHz 2 cores of 2495 MHz already using the old LLR1 [must switch to LLR2, for double check purposes] already using the old NewPGen for sieve, the same speed as the new sieves like SrSieve [all the sieves are stopped] [must switch to FermFact.exe which is a milion times faster, but have some bugs]
[check Caldwell's and Keller's lists] (PrimePages) (kkk<300) (5-5.5M Nov 2024)(5.5-6M Mar 2025) 277*2^5185268+1 1560924 L5888 2024-07-03 227*2^5213195+1 1569331 L5517 2024-07-18 273*2^5242597+1 1578182 L5192 2024-08-09 247*2^5254234+1 1581685 L5923 2024-08-09 221*2^5284643+1 1590839 L5517 2024-08-23 237*2^5291999+1 1593053 L5532 2024-08-25 237*2^5315983+1 1600273 L6064 2024-09-02 245*2^5404089+1 1626796 L5282 2024-09-28 285*2^5408709+1 1628187 L5178 2024-10-01 247*2^5477512+1 1648898 L5373 2024-10-22 205*2^5532904+1 1665573 L5517 2024-11-13 205*2^5805562+1 1747651 L5261 2025-01-16 131*2^5013361+1 1509175 L5178 2024-05-04 183*2^5042357+1 1517903 L5178 2024-05-13 175*2^5049344+1 1520007 L5178 2024-05-15 181*2^5057960+1 1522600 L5178 2024-05-17 147*2^5146964+1 1549393 L5559 2024-06-17 125*2^5149981+1 1550301 L6042 2024-06-19 149*2^5196375+1 1564267 L5174 2024-07-09 131*2^5298475+1 1595003 L5517 2024-08-26 153*2^5369765+1 1616463 L5969 2024-09-16 127*2^5391378+1 1622969 L5178 2024-09-21 147*2^5410159+1 1628623 L5517 2024-10-01 165*2^5416628+1 1630570 L5537 2024-10-06 193*2^5431414+1 1635021 L5214 2024-10-10 159*2^5432226+1 1635266 L6082 2024-10-10 129*2^5453363+1 1641628 L6083 2024-10-16 191*2^5531015+1 1665004 L5517 2024-11-09 163*2^5550632+1 1670909 L5517 2024-11-13 141*2^5600116+1 1685806 L6089 2024-11-26 165*2^5633373+1 1695817 L5178 2024-12-03 101*2^5774879+1 1738414 L5537 2025-01-09 183*2^5814122+1 1750228 L5612 2025-01-20 195*2^5841059+1 1758337 L5178 2025-01-27 135*2^5854694+1 1762441 L5997 2025-02-02 179*2^5894939+1 1774556 L5261 2025-02-04 189*2^5932506+1 1785865 L5995 2025-02-09 163*2^5945098+1 1789656 L5554 2025-02-10 53*2^5019181+1 1510926 L4965 2023-07-19 81*2^5100331+1 1535355 L4965 2022-08-23 81*2^5115131+1 1539810 L4965 2022-08-24 39*2^5119458+1 1541113 L1204 2019-11-24 27*2^5213635+1 1569462 L3760 2015-03-12 45*2^5308037+1 1597881 L4761 2019-12-21 93*2^5323466+1 1602525 L5537 2024-09-06 77*2^5422903+1 1632459 A2 2024-07-06 91*2^5435752+1 1636327 L5214 2024-10-10 89*2^5519481+1 1661532 L5178 2024-11-05 13*2^5523860+1 1662849 L1204 2020-01-23 31*2^5560820+1 1673976 L1204 2020-01-28 81*2^5600028+1 1685779 L4965 2022-08-25 65*2^5671355+1 1707250 L5294 2024-12-12 41*2^5651731+1 1701343 L1204 2020-02-16 57*2^5759943+1 1733918 L5517 2025-01-03 57*2^5785428+1 1741590 L5302 2025-01-10 99*2^5798449+1 1745510 L5517 2025-01-14 91*2^5960816+1 1794387 L5969 2025-02-11 55*2^5982526+1 1800922 L5554 2025-02-14
(Primecrunch) andy@primecrunch.com [primegrid]