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CRUS Liskovets-Gallot

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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

Odd n's

Proth values

Even n's

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

Odd n's

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

Notes

  1. Problem 36 "The Liskovets-Gallot numbers" from PP&P connection by Carlos Rivera
  2. 2.0 2.1 A Liskovets-Gallot theorem proven! by Jean Penné, 2015-08-02


Links