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# CRUS Liskovets-Gallot

CRUS Liskovets-Gallot is a Conjectures 'R Us (CRUS) subproject aiming to prove the Liskovets-Gallot conjectures, which relate to the smallest Riesel and Proth k-values, divisible by 3, with no primes for n-values of a given parity.

## Explanations

Main article: Liskovets-Gallot conjectures

Valery Liskovets first observed in 2001 that some k-values, divisible by 3, had few prime n-values of a given parity. He then conjectured that there existed k-values (initially for Proth primes, then also for Riesel primes), divisible by 3, that had no primes of a given parity. This was proven by Yves Gallot, who provided examples for all four cases (Riesel/Proth, even/odd). Gallot further conjectured that these four examples are the smallest such k-values of each type, not including algebraic factorizations.[1]

This subproject is attempting to prove the latter set of conjectures by finding primes for n-values of the required sign (Riesel/Proth) and parity (even/odd). The process is the same as PrimeGrid's subprojects for The Riesel Problem and Seventeen or Bust.

## History

This subproject was founded by Conjectures 'R Us in January 2008, as an extension of the base 4 Riesel and Sierpiński problems. The initial search was led by Jean Penné and Gary Barnes, and a page for the effort was created on the Riesel and Proth Prime Database on January 11.

The even Proth conjecture was proven on 2015-08-02, by Penné, and the discovery was made public a day later after a personal double-check.[2]

## Current status

### Riesel values

#### Even n's

• k=9519, done to n=16777216 (even n-values only), not reserved
• k=14361

### Proth values

#### Even n's

The even n conjecture was proven in August 2015.[2]

## Primes found

### Riesel

#### Even n's

The data file can be found here.

Date Finder Number k n

2008-01-19 Jean Penné 2181•237890-1 2181 37890
2008-01-19 Jean Penné 6549•25076-1 6549 5076
2008-01-19 Jean Penné 8181•28018-1 8181 8018
2008-01-19 Jean Penné 8961•230950-1 8961 30950
2008-01-19 Jean Penné 11379•232252-1 11379 32252
2008-01-19 Jean Penné 12849•29788-1 12849 9788
2008-01-19 Jean Penné 14859•211228-1 14859 11228
2008-01-19 Jean Penné 15639•266328-1 15639 66328
2008-01-19 Jean Penné 16431•24198-1 16431 4198
2008-01-19 Jean Penné 17889•210628-1 17889 10628
2015-06-13 Gary Barnes 19401•23086450-1 19401 3086450
2011-06-02 Ian M. Gunn 20049•21687252-1 20049 1687252
2008-01-19 Jean Penné 21501•27286-1 21501 7286
2008-01-19 Jean Penné 26091•24198-1 26091 4198
2008-01-19 Jean Penné 26511•2167154-1 26511 167154
2008-01-19 Jean Penné 26601•246246-1 26601 46246
2008-01-19 Jean Penné 30171•276286-1 30171 76286
2008-01-19 Jean Penné 31431•216942-1 31431 16942
2008-01-19 Jean Penné 31749•25040-1 31749 5040
2008-01-19 Jean Penné 31959•219704-1 31959 19704
2008-01-19 Jean Penné 35259•210540-1 35259 10540

#### Odd n's

The data file can be found here.

Date Finder Number k n

2008-01-19 Jean Penné 903•210227-1 903 10227
2008-01-19 Jean Penné 4887•24289-1 4887 4289
2008-01-19 Jean Penné 5007•26765-1 5007 6765
2008-01-19 Jean Penné 5163•26183-1 5163 6183
2008-05-23 Gary Barnes 6927•2743481-1 6927 743481
2008-01-19 Jean Penné 7977•231265-1 7977 31265
2008-01-28 Gary Barnes 8367•2313705-1 8367 313705
2008-01-19 Jean Penné 9087•24741-1 9087 4741
2008-01-19 Jean Penné 10113•214535-1 10113 14535
2008-01-19 Jean Penné 15213•220311-1 15213 20311
2008-01-19 Jean Penné 19377•218677-1 19377 18677
2008-01-19 Jean Penné 21813•24283-1 21813 4283
2008-01-19 Jean Penné 22863•2101135-1 22863 101135
2008-01-19 Jean Penné 27957•221477-1 27957 21477
2008-12-03 Karsten Bonath 30003•2613463-1 30003 613463
2008-01-19 Jean Penné 30357•265361-1 30357 65361
2008-01-19 Jean Penné 32937•28473-1 32937 8473
2008-01-19 Jean Penné 33837•24273-1 33837 4273
2008-01-19 Jean Penné 34533•232899-1 34533 32899
2008-01-19 Jean Penné 35193•212483-1 35193 12483
2008-01-19 Jean Penné 44283•24439-1 44283 4439
2008-01-19 Jean Penné 46107•24277-1 46107 4277
2008-01-22 Jean Penné 46923•265175-1 46923 65175
2008-01-21 Jean Penné 48927•235861-1 48927 35861
2008-01-19 Jean Penné 52137•226309-1 52137 26309
2008-01-21 Karsten Bonath 53973•2198575-1 53973 198575
2008-01-19 Jean Penné 55983•29851-1 55983 9851
2008-01-19 Jean Penné 56493•26891-1 56493 6891
2008-01-21 Jean Penné 59655•243825-1 59655 43825
2008-01-19 Jean Penné 59763•24611-1 59763 4611
2008-01-19 Jean Penné 61833•24651-1 61833 4651
2008-01-19 Jean Penné 63153•260295-1 63153 60295
2008-01-19 Jean Penné 64023•211431-1 64023 11431
2008-01-19 Jean Penné 67737•24437-1 67737 4437
2008-01-19 Jean Penné 70743•249387-1 70743 49387
2008-01-19 Jean Penné 72327•217125-1 72327 17125
2008-01-19 Jean Penné 72993•223319-1 72993 23319
2008-01-19 Jean Penné 75093•215371-1 75093 15371
2008-01-22 Jean Penné 75363•2120595-1 75363 120595
2008-01-19 Jean Penné 75387•25181-1 75387 5181
2008-01-22 Jean Penné 75873•262419-1 75873 62419
2008-01-19 Jean Penné 78933•211443-1 78933 11443
2008-01-22 Jean Penné 79437•235093-1 79437 35093
2008-01-19 Jean Penné 84807•247389-1 84807 47389
2008-03-28 Jean Penné 86613•2356967-1 86613 356967
2008-01-19 Jean Penné 87735•24551-1 87735 4551
2008-01-19 Jean Penné 88623•213251-1 88623 13251
2008-01-19 Jean Penné 88743•24619-1 88743 4619
2008-01-19 Jean Penné 90567•26577-1 90567 6577
2008-01-19 Jean Penné 91671•28795-1 91671 8795
2008-01-19 Jean Penné 93507•25449-1 93507 5449
2008-01-19 Jean Penné 97323•252207-1 97323 52207
2008-03-31 Karsten Bonath 99363•2268879-1 99363 268879
2008-01-19 Jean Penné 100053•228459-1 100053 28459
2008-01-19 Jean Penné 100353•25147-1 100353 5147
2008-01-28 Jean Penné 100377•2231813-1 100377 231813
2008-01-19 Jean Penné 101823•24519-1 101823 4519
2008-01-19 Jean Penné 102993•248975-1 102993 48975
2008-01-19 Jean Penné 105123•25555-1 105123 5555
2008-01-19 Jean Penné 105837•25913-1 105837 5913
2008-11-17 Karsten Bonath 106377•2475569-1 106377 475569
2008-01-22 Jean Penné 114249•248469-1 114249 48469
2008-01-19 Jean Penné 115167•28685-1 115167 8685
2008-01-19 Jean Penné 117303•24451-1 117303 4451
2008-01-19 Jean Penné 117867•24513-1 117867 4513
2008-01-19 Jean Penné 120387•25645-1 120387 5645
2008-01-19 Jean Penné 121557•211817-1 121557 11817
2008-01-19 Jean Penné 129747•218657-1 129747 18657
2008-01-24 Jean Penné 130383•2104123-1 130383 104123
2008-03-31 Karsten Bonath 130467•2273437-1 130467 273437
2008-01-24 Jean Penné 131727•2169621-1 131727 169621
2008-01-19 Jean Penné 132507•24485-1 132507 4485
2008-01-19 Jean Penné 133023•29087-1 133023 9087
2008-12-05 Jean Penné 133977•2811485-1 133977 811485
2008-01-19 Jean Penné 134037•24421-1 134037 4421
2008-01-24 Jean Penné 135567•268325-1 135567 68325
2008-01-19 Jean Penné 142683•222371-1 142683 22371
2008-02-18 Jean Penné 144117•2224977-1 144117 224977
2008-01-19 Jean Penné 144393•26567-1 144393 6567
2008-01-19 Jean Penné 144957•26473-1 144957 6473
2008-04-07 Jean Penné 145257•2443077-1 145257 443077
2009-01-19 Karsten Bonath 147687•2843689-1 147687 843689
2008-01-19 Jean Penné 148227•25997-1 148227 5997
2011-07-29 Max Dettweiler 148323•21973319-1 148323 1973319
2008-01-19 Jean Penné 148803•225019-1 148803 25019
2008-01-19 Jean Penné 152907•24365-1 152907 4365
2008-01-19 Jean Penné 154827•29113-1 154827 9113
2014-11-10 Gary Barnes 155877•22273465-1 155877 2273465
2008-01-19 Jean Penné 157383•244059-1 157383 44059
2008-01-28 Jean Penné 161583•2138711-1 161583 138711
2008-01-19 Jean Penné 167007•24901-1 167007 4901
2008-01-19 Jean Penné 167997•218705-1 167997 18705
2008-01-19 Jean Penné 169527•29329-1 169527 9329
2008-01-19 Jean Penné 169743•223791-1 169743 23791
2008-01-19 Jean Penné 170223•24187-1 170223 4187
2008-01-19 Jean Penné 170733•27307-1 170733 7307
2008-01-19 Jean Penné 171783•26759-1 171783 6759
2008-04-02 Karsten Bonath 172167•2282649-1 172167 282649

### Proth

#### Even n's

The data file can be found here.

Date Finder Number k n

2008-01-16 Jean Penné 2379•28114+1 2379 8114
2005-02-01 Harsh Aggarwal 8139•225954+1 8139 25954
2008-01-16 Jean Penné 9609•25422+1 9609 5422
2008-01-16 Jean Penné 10281•27444+1 10281 7444
2008-01-16 Jean Penné 11709•26882+1 11709 6882
2008-01-16 Jean Penné 12711•25092+1 12711 5092
2005-01-27 Jean Penné 14661•291368+1 14661 91368
2005-01-27 Darren Wallace 15441•220584+1 15441 20584
2008-01-16 Jean Penné 17169•26450+1 17169 6450
2005-01-27 Darren Wallace 21069•223006+1 21069 23006
2005-01-27 Darren Wallace 21699•272874+1 21699 72874
2015-08-03 Jean Penné 23451•23739388+1 23451 3739388
2005-01-29 Kenneth J. Brazier 23799•2105890+1 23799 105890
2008-01-16 Jean Penné 23901•211292+1 23901 11292
2005-01-28 (Mark) 30579•248594+1 30579 48594
2005-01-29 Jean Penné 33771•2178200+1 33771 178200
2005-06-20 Darren Wallace 33879•2378022+1 33879 378022
2008-01-16 Jean Penné 35889•27770+1 35889 7770
2008-01-16 Jean Penné 39231•213716+1 39231 13716
2008-01-16 Jean Penné 39759•24594+1 39759 4594
2008-01-16 Jean Penné 40269•28458+1 40269 8458
2008-01-16 Jean Penné 41289•213514+1 41289 13514
2005-01-29 Geoffrey Reynolds 41709•280594+1 41709 80594
2005-10-14 Jean Penné 42717•2905792+1 42717 905792
2008-01-16 Jean Penné 44469•213134+1 44469 13134
2005-01-31 Thomas Masser 51171•293736+1 51171 93736
2008-01-16 Jean Penné 52419•24578+1 52419 4578
2008-01-16 Jean Penné 52701•26976+1 52701 6976
2005-01-27 Thomas Masser 52839•232558+1 52839 32558
2008-01-16 Jean Penné 53979•27590+1 53979 7590
2005-01-29 Harsh Aggarwal 55611•240212+1 55611 40212
2008-01-16 Jean Penné 56019•28094+1 56019 8094
2008-01-16 Jean Penné 56139•24858+1 56139 4858
2005-01-27 (Mystwalker) 58791•279420+1 58791 79420
2014-02-14 Jean Penné 60849•23067914+1 60849 3067914
2005-01-29 Jean Penné 60891•240144+1 60891 40144
2008-01-16 Jean Penné 61371•212576+1 61371 12576
2008-01-16 Jean Penné 62391•25472+1 62391 5472
2005-01-31 Darren Wallace 63411•272064+1 63411 72064

#### Odd n's

The data file can be found here.

Date Finder Number k n

2008-01-15 Jean Penné 93•220917+1 93 20917
2005-02-06 Jean Penné 2943•2108041+1 2943 108041
2008-01-15 Jean Penné 5193•24277+1 5193 4277
2008-01-15 Jean Penné 5703•25149+1 5703 5149
2008-01-15 Jean Penné 5823•28105+1 5823 8105
2008-01-15 Jean Penné 6807•24415+1 6807 4415
2008-01-15 Jean Penné 6843•214753+1 6843 14753
2008-01-15 Jean Penné 7233•24277+1 7233 4277
2008-01-15 Jean Penné 9777•218975+1 9777 18975
2008-01-15 Jean Penné 10923•26801+1 10923 6801
2008-01-15 Jean Penné 14397•24347+1 14397 4347
2008-01-15 Jean Penné 16917•212799+1 16917 12799
2005-01-28 Tyler Cadigan 17457•229563+1 17457 29563
2005-01-28 Tyler Cadigan 17937•253927+1 17937 53927
2008-01-15 Jean Penné 20997•28191+1 20997 8191
2005-01-27 (Mark) 22653•228969+1 22653 28969
2005-05-25 Darren Wallace 24693•2357417+1 24693 357417
2005-01-27 (Mark) 25083•224981+1 25083 24981
2008-01-15 Jean Penné 25917•29671+1 25917 9671
2008-01-15 Jean Penné 26613•289749+1 26613 89749
2008-01-15 Jean Penné 30933•24433+1 30933 4433
2008-01-15 Jean Penné 35787•236639+1 35787 36639
2008-02-14 Gary Barnes 37953•2298913+1 37953 298913
2008-01-15 Gary Barnes 38463•258753+1 38463 58753
2008-01-20 Gary Barnes 39297•2169495+1 39297 169495
2008-01-15 Jean Penné 40857•25383+1 40857 5383
2008-01-15 Jean Penné 42993•216165+1 42993 16165
2008-01-15 Jean Penné 43167•29795+1 43167 9795
2008-01-15 Jean Penné 46623•279553+1 46623 79553
2008-01-15 Jean Penné 49563•25813+1 49563 5813
2008-01-20 Gary Barnes 50433•2156597+1 50433 156597
2008-01-15 Jean Penné 60273•27421+1 60273 7421
2011-06-01 Max Dettweiler 60357•21676907+1 60357 1676907
2008-01-15 Gary Barnes 60963•273409+1 60963 73409
2008-01-20 Gary Barnes 61137•2162967+1 61137 162967
2008-01-15 Gary Barnes 62307•244559+1 62307 44559
2008-01-15 Jean Penné 63357•24211+1 63357 4211
2008-01-15 Jean Penné 65223•24189+1 65223 4189
2008-01-15 Jean Penné 65253•210301+1 65253 10301
2008-01-15 Jean Penné 67917•213079+1 67917 13079
2008-01-15 Jean Penné 69963•25205+1 69963 5205
2008-02-11 Gary Barnes 70467•2268503+1 70467 268503
2008-01-15 Jean Penné 72537•215771+1 72537 15771
2008-01-15 Jean Penné 73023•217965+1 73023 17965
2008-01-15 Gary Barnes 75183•235481+1 75183 35481
2008-01-15 Jean Penné 78543•210089+1 78543 10089
2008-01-15 Gary Barnes 78753•263761+1 78753 63761
2008-03-31 Gary Barnes 80463•2468141+1 80463 468141
2008-01-15 Jean Penné 80517•25423+1 80517 5423
2008-01-15 Jean Penné 81147•217615+1 81147 17615
2008-01-15 Jean Penné 82197•25079+1 82197 5079
2014-10-20 Gary Barnes 84363•22222321+1 84363 2222321
2011-06-02 Lennart Vogel 85287•21890011+1 85287 1890011
2008-01-15 Jean Penné 88863•29825+1 88863 9825
2008-01-15 Jean Penné 91383•215333+1 91383 15333
2008-01-20 Gary Barnes 91437•2161615+1 91437 161615
2008-01-15 Jean Penné 93033•230473+1 93033 30473
2008-01-15 Gary Barnes 93477•263251+1 93477 63251
2008-01-15 Gary Barnes 93663•282317+1 93663 82317

## Notes

1. Problem 36 "The Liskovets-Gallot numbers" from PP&P connection by Carlos Rivera
2. A Liskovets-Gallot theorem proven! by Jean Penné, 2015-08-02