Difference between revisions of "Riesel prime 3 2"

Latest revision as of 06:19, 14 November 2024

Current data

`k` , `b` :	2 , 3
Count :	38
Nash :	2685
Max `n` :	2,000,000
Date :	2024-08-01

1^[1], 2^[2], 3^[3], 7^[4], 8^[5], 12^[6], 20^[7], 23, 27, 35, 56^[8], 62, 68, 131, 222, 384, 387, 579, 644, 1772, 3751, 5270, 6335, 8544, 9204, 12312, 18806, 21114, 49340, 75551, 90012, 128295, 143552, 147488, 1010743, 1063844, 1360104, 2834778

Remarks :

See H.C.Williams, C.R.Zarnke: "Some prime numbers of the forms 2A3^n+1 and 2A3^n-1" Math. Comp. 26 (1972), 995-998
The sequence A003307 in OEIS
See also Williams 2•3ⁿ-1

Notes

History

2024-08-01: Found n = 2834778, Ryan Propper
2021-01-26: Checked to n = 2000000, Borys Jaworski, released
2020-04-04: Checked to n = 2000000, Borys Jaworski
2020-01-03: Checked n = 1940000 - 2000000, Borys Jaworski
2019-10-05: Checked n = 1930000 - 1940000, Borys Jaworski
2019-09-05: Checked n = 1840000 - 1930000, Borys Jaworski
2019-03-01: Checked n = 1810000 - 1840000, Borys Jaworski
2019-01-01: Checked n = 1800000 - 1810000, Borys Jaworski
2018-11-30: Checked n = 1780000 - 1800000, Borys Jaworski
2018-11-01: Checked n = 1760000 - 1780000, Borys Jaworski
2018-09-02: Checked n = 1720000 - 1760000, Borys Jaworski
2018-05-03: Checked n = 1690000 - 1720000, Borys Jaworski
2018-02-02: Checked n = 1680000 - 1690000, Borys Jaworski
2018-01-01: Checked n = 1670000 - 1680000, Borys Jaworski
2017-12-02: Checked n = 1660000 - 1670000, Borys Jaworski
2017-10-27: Checked n = 1630000 - 1660000, Borys Jaworski
2017-07-02: Checked n = 1610000 - 1630000, Borys Jaworski
2017-05-02: Checked n = 1600000 - 1610000, Borys Jaworski
2017-04-01: Checked n = 1570000 - 1600000, Borys Jaworski
2017-01-31: Checked n = 1560000 - 1570000, Borys Jaworski
2017-01-01: Checked n = 1550000 - 1560000, Borys Jaworski
2016-11-30: Checked to n = 1550000, Borys Jaworski
2016-11-01: Checked to n = 1550000, Borys Jaworski
2016-10-01: Checked to n = 1550000, Borys Jaworski
2016-08-31: Checked n = 1540000 - 1550000, Borys Jaworski
2016-07-01: Checked n = 1530000 - 1540000, Borys Jaworski
2016-06-01: Checked n = 1510000 - 1530000, Borys Jaworski
2016-04-30: Checked n = 1490000 - 1510000, Borys Jaworski
2016-03-31: Checked n = 1480000 - 1490000, Borys Jaworski
2016-02-29: Checked n = 1470000 - 1480000, Borys Jaworski
2016-02-01: Checked n = 1450000 - 1470000, Borys Jaworski
2016-01-03: Checked n = 1430000 - 1450000, Borys Jaworski
2015-11-30: Checked n = 1420000 - 1430000, Borys Jaworski
2015-10-31: Checked n = 1390000 - 1420000, Borys Jaworski
2015-08-31: Checked n = 1350000 - 1390000, Borys Jaworski
2015-07-31: Found n = 1360104, Borys Jaworski
2015-06-01: Checked to n = 1350000, Borys Jaworski
2015-05-01: Checked to n = 1350000, Borys Jaworski
2015-03-31: Checked n = 1340000 - 1350000, Borys Jaworski
2015-02-28: Checked n = 1330000 - 1340000, Borys Jaworski
2015-02-01: Checked n = 1320000 - 1330000, Borys Jaworski
2015-01-03: Checked n = 1300000 - 1320000, Borys Jaworski
2014-11-01: Checked n = 1290000 - 1300000, Borys Jaworski
2014-09-30: Checked n = 1270000 - 1290000, Borys Jaworski
2014-07-30: Checked n = 1260000 - 1270000, Borys Jaworski
2014-06-30: Checked n = 1250000 - 1260000, Borys Jaworski
2014-05-01: Checked n = 1240000 - 1250000, Borys Jaworski
2014-03-31: Checked to n = 1240000, Borys Jaworski
2014-03-01: Checked n = 1220000 - 1240000, Borys Jaworski
2013-11-30: Checked n = 1210000 - 1220000, Borys Jaworski
2013-10-31: Checked n = 1200000 - 1210000, Borys Jaworski
2013-09-30: Checked n = 1190000 - 1200000, Borys Jaworski
2013-07-31: Checked to n = 1190000, Borys Jaworski
2013-07-01: Checked n = 1180000 - 1190000, Borys Jaworski
2013-06-02: Checked to n = 1180000, Borys Jaworski
2013-04-01: Checked n = 1170000 - 1180000, Borys Jaworski
2013-03-02: Checked to n = 1170000, Borys Jaworski
2013-01-31: Checked n = 1150000 - 1170000, Borys Jaworski
2012-12-01: Checked to n = 1150000, Borys Jaworski
2012-11-01: Checked n = 1140000 - 1150000, Borys Jaworski
2012-09-30: Checked n = 1130000 - 1140000, Borys Jaworski
2012-08-30: Checked n = 990000 - 1130000, Borys Jaworski
2012-02-12: Found n = 1063844, Borys Jaworski
2011-09-01: Found n = 1010743, Borys Jaworski
2011-09-01: Checked n = 315000 - 990000, Borys Jaworski
2009-04-12: Checked n = 400000 - 570000, David Broadhurst
2009-03-09: Checked n = 189000 - 400000, David Broadhurst
2008-03-10: Checked to n = 315000, Borys Jaworski
2008-01-05: Checked n = 100000 - 150000?, Herman Jamke
2005-08-24: Checked n = 10000 - 100000?, T. D. Noe
2004-08-15: Found n = 147488, Ingo Buechel, Wilfrid Keller
2004-08-12: Found n = 143552, Ingo Buechel, Wilfrid Keller
2003-06-20: Found n = 128295, Ingo Buechel, Wilfrid Keller
2001-09-28: Found n = 90012, Wilfrid Keller
2001-08-12: Found n = 75551, Wilfrid Keller
2001-06-30: Found n = 49340, Wilfrid Keller
1999-12-11: Checked n = 326 - 10000?, Douglas Burke
1972-10: Checked n = 1 - 325, Hugh C. Williams, Charles R. Zarnke

[1] Twin n=1, Near Woodall 2•3¹-1

[2] Twin n=2, Woodall 2•3²-1

[3] Near Woodall 2•3³-1

[4] Woodall 6•3⁶-1

[5] Woodall 2•81²-1, Near Woodall 6•3⁷-1

[6] Woodall 2•729²-1

[7] Woodall 18•3¹⁸-1

[8] Woodall 18•27¹⁸-1, Near Woodall 54•3⁵³-1

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

@@ Line 2: / Line 2: @@
 |Rk=2
 |Rb=3
-|RCount=37
+|RCount=38
 |RNash=2685
 |RMaxn=2000000
-|RDate=2021-01-26
+|RDate=2024-08-01
 |RReserved=
 |RMultiRes=
 |RNlist=
+;T:T;C:{{NWo|+|3|1}}
-;C:{{NWo|3|2}}
+;T:T;C:{{NWo|3|2}}
+;C:{{NWo|-|3|3}}
 ;C:{{NWo|3|6}}
-;C:{{NWo|81|2}}
+;C:{{NWo|81|2}}, {{NWo|-|3|7}}
 ;C:{{NWo|729|2}}
 ;C:{{NWo|3|18}}
@@ Line 19: / Line 19: @@
+;C:{{NWo|27|18}}, {{NWo|+|3|53}}
@@ Line 46: / Line 46: @@
 1063844;104556
 1360104;120178
+2834778;138366
 |RRemarks=See [http://www.ams.org/journals/mcom/1972-26-120/S0025-5718-1972-0314747-X/S0025-5718-1972-0314747-X.pdf H.C.Williams, C.R.Zarnke: "Some prime numbers of the forms 2A3^n+1 and 2A3^n-1"] Math. Comp. 26 (1972), 995-998<br>The {{OEIS|l|A003307}}<br>See also {{NWi|MM|3|n}}
 |RSieve=
 }}
 ==History==
+{{HistF|2024-08-01|2834778|Ryan Propper}}
 {{HistC|2021-01-26|2000000|Borys Jaworski|570134}}, released
 {{HistC|2020-04-04|2000000|Borys Jaworski|541720}}
-{{HistC|2020-01-03|2000000|Borys Jaworski|534151}}
+{{HistC|2020-01-03|1940000-2000000|Borys Jaworski|534151}}
-{{HistC|2019-10-05|1940000|Borys Jaworski|527377}}
+{{HistC|2019-10-05|1930000-1940000|Borys Jaworski|527377}}
-{{HistC|2019-09-05|1930000|Borys Jaworski|525231}}
+{{HistC|2019-09-05|1840000-1930000|Borys Jaworski|525231}}
-{{HistC|2019-03-01|1840000|Borys Jaworski|509799}}
+{{HistC|2019-03-01|1810000-1840000|Borys Jaworski|509799}}
-{{HistC|2019-01-01|1810000|Borys Jaworski|504585}}
+{{HistC|2019-01-01|1800000-1810000|Borys Jaworski|504585}}
-{{HistC|2018-11-30|1800000|Borys Jaworski|501366}}
+{{HistC|2018-11-30|1780000-1800000|Borys Jaworski|501366}}
-{{HistC|2018-11-01|1780000|Borys Jaworski|499245}}
+{{HistC|2018-11-01|1760000-1780000|Borys Jaworski|499245}}
-{{HistC|2018-09-02|1760000|Borys Jaworski|495144}}
+{{HistC|2018-09-02|1720000-1760000|Borys Jaworski|495144}}
-{{HistC|2018-05-03|1720000|Borys Jaworski|486855}}
+{{HistC|2018-05-03|1690000-1720000|Borys Jaworski|486855}}
-{{HistC|2018-02-02|1690000|Borys Jaworski|479098}}
+{{HistC|2018-02-02|1680000-1690000|Borys Jaworski|479098}}
-{{HistC|2018-01-01|1680000|Borys Jaworski|475835}}
+{{HistC|2018-01-01|1670000-1680000|Borys Jaworski|475835}}
-{{HistC|2017-12-02|1670000|Borys Jaworski|472955}}
+{{HistC|2017-12-02|1660000-1670000|Borys Jaworski|472955}}
-{{HistC|2017-10-27|1660000|Borys Jaworski|470445}}
+{{HistC|2017-10-27|1630000-1660000|Borys Jaworski|470445}}
-{{HistC|2017-07-02|1630000|Borys Jaworski|462571}}
+{{HistC|2017-07-02|1610000-1630000|Borys Jaworski|462571}}
-{{HistC|2017-05-02|1610000|Borys Jaworski|458066}}
+{{HistC|2017-05-02|1600000-1610000|Borys Jaworski|458066}}
-{{HistC|2017-04-01|1600000|Borys Jaworski|455930}}
+{{HistC|2017-04-01|1570000-1600000|Borys Jaworski|455930}}
-{{HistC|2017-01-31|1570000|Borys Jaworski|451914}}
+{{HistC|2017-01-31|1560000-1570000|Borys Jaworski|451914}}
-{{HistC|2017-01-01|1560000|Borys Jaworski|450240}}
+{{HistC|2017-01-01|1550000-1560000|Borys Jaworski|450240}}
 {{HistC|2016-11-30|1550000|Borys Jaworski|448105}}
 {{HistC|2016-11-01|1550000|Borys Jaworski|446236}}
 {{HistC|2016-10-01|1550000|Borys Jaworski|443995}}
-{{HistC|2016-08-31|1550000|Borys Jaworski|441259}}
+{{HistC|2016-08-31|1540000-1550000|Borys Jaworski|441259}}
-{{HistC|2016-07-01|1540000|Borys Jaworski|437306}}
+{{HistC|2016-07-01|1530000-1540000|Borys Jaworski|437306}}
-{{HistC|2016-06-01|1530000|Borys Jaworski|435321}}
+{{HistC|2016-06-01|1510000-1530000|Borys Jaworski|435321}}
-{{HistC|2016-04-30|1510000|Borys Jaworski|432867}}
+{{HistC|2016-04-30|1490000-1510000|Borys Jaworski|432867}}
-{{HistC|2016-03-31|1490000|Borys Jaworski|430460}}
+{{HistC|2016-03-31|1480000-1490000|Borys Jaworski|430460}}
-{{HistC|2016-02-29|1480000|Borys Jaworski|427810}}
+{{HistC|2016-02-29|1470000-1480000|Borys Jaworski|427810}}
-{{HistC|2016-02-01|1470000|Borys Jaworski|424796}}
+{{HistC|2016-02-01|1450000-1470000|Borys Jaworski|424796}}
-{{HistC|2016-01-03|1450000|Borys Jaworski|421052}}
+{{HistC|2016-01-03|1430000-1450000|Borys Jaworski|421052}}
-{{HistC|2015-11-30|1430000|Borys Jaworski|417816}}
+{{HistC|2015-11-30|1420000-1430000|Borys Jaworski|417816}}
-{{HistC|2015-10-31|1420000|Borys Jaworski|414440}}
+{{HistC|2015-10-31|1390000-1420000|Borys Jaworski|414440}}
-{{HistC|2015-08-31|1390000|Borys Jaworski|409295}}
+{{HistC|2015-08-31|1350000-1390000|Borys Jaworski|409295}}
-{{HistF|2015-07-31|1360104|Borys Jaworski}}
+{{HistF|2015-07-31|1360104|Borys Jaworski|407006}}
 {{HistC|2015-06-01|1350000|Borys Jaworski|403375}}
 {{HistC|2015-05-01|1350000|Borys Jaworski|401416}}
-{{HistC|2015-03-31|1350000|Borys Jaworski|399036}}
+{{HistC|2015-03-31|1340000-1350000|Borys Jaworski|399036}}
-{{HistC|2015-02-28|1340000|Borys Jaworski|396676}}
+{{HistC|2015-02-28|1330000-1340000|Borys Jaworski|396676}}
-{{HistC|2015-02-01|1330000|Borys Jaworski|394134}}
+{{HistC|2015-02-01|1320000-1330000|Borys Jaworski|394134}}
-{{HistC|2015-01-03|1320000|Borys Jaworski|391520}}
+{{HistC|2015-01-03|1300000-1320000|Borys Jaworski|391520}}
-{{HistC|2014-11-01|1300000|Borys Jaworski|386684}}
+{{HistC|2014-11-01|1290000-1300000|Borys Jaworski|386684}}
-{{HistC|2014-09-30|1290000|Borys Jaworski|384129}}
+{{HistC|2014-09-30|1270000-1290000|Borys Jaworski|384129}}
-{{HistC|2014-07-30|1270000|Borys Jaworski|379392}}
+{{HistC|2014-07-30|1260000-1270000|Borys Jaworski|379392}}
-{{HistC|2014-06-30|1260000|Borys Jaworski|377076}}
+{{HistC|2014-06-30|1250000-1260000|Borys Jaworski|377076}}
-{{HistC|2014-05-01|1250000|Borys Jaworski|372409}}
+{{HistC|2014-05-01|1240000-1250000|Borys Jaworski|372409}}
 {{HistC|2014-03-31|1240000|Borys Jaworski|370057}}
-{{HistC|2014-03-01|1240000|Borys Jaworski|368017}}
+{{HistC|2014-03-01|1220000-1240000|Borys Jaworski|368017}}
-{{HistC|2013-11-30|1220000|Borys Jaworski|360731}}
+{{HistC|2013-11-30|1210000-1220000|Borys Jaworski|360731}}
-{{HistC|2013-10-31|1210000|Borys Jaworski|358080}}
+{{HistC|2013-10-31|1200000-1210000|Borys Jaworski|358080}}
-{{HistC|2013-09-30|1200000|Borys Jaworski|354690}}
+{{HistC|2013-09-30|1190000-1200000|Borys Jaworski|354690}}
 {{HistC|2013-07-31|1190000|Borys Jaworski|347910}}
-{{HistC|2013-07-01|1190000|Borys Jaworski|344949}}
+{{HistC|2013-07-01|1180000-1190000|Borys Jaworski|344949}}
 {{HistC|2013-06-02|1180000|Borys Jaworski|342368}}
-{{HistC|2013-04-01|1180000|Borys Jaworski|335709}}
+{{HistC|2013-04-01|1170000-1180000|Borys Jaworski|335709}}
 {{HistC|2013-03-02|1170000|Borys Jaworski|331612}}
-{{HistC|2013-01-31|1170000|Borys Jaworski|326844}}
+{{HistC|2013-01-31|1150000-1170000|Borys Jaworski|326844}}
 {{HistC|2012-12-01|1150000|Borys Jaworski|320163}}
-{{HistC|2012-11-01|1150000|Borys Jaworski|316587}}
+{{HistC|2012-11-01|1140000-1150000|Borys Jaworski|316587}}
-{{HistC|2012-09-30|1140000|Borys Jaworski|313240}}
+{{HistC|2012-09-30|1130000-1140000|Borys Jaworski|313240}}
-{{HistC|2012-08-30|1130000|Borys Jaworski|309790}}
+{{HistC|2012-08-30|990000-1130000|Borys Jaworski|309790}}
-{{HistF|2012-02-12|1063844|Borys Jaworski}}
+{{HistF|2012-02-12|1063844|Borys Jaworski|289137}}
-{{HistF|2011-09-01|1010743|Borys Jaworski}}
+{{HistF|2011-09-01|1010743|Borys Jaworski|270574}}
-{{HistC|2009-04-12|570000|David Broadhurst}}
+{{HistC|2011-09-01|315000-990000|Borys Jaworski|270574}}
-{{HistC|2009-03-09|189000 - 400000|David Broadhurst}}
+{{HistC|2009-04-12|400000-570000|David Broadhurst}}
+{{HistC|2009-03-09|189000-400000|David Broadhurst}}
+{{HistC|2008-03-10|315000|Borys Jaworski|128327}}
+{{HistC|2008-01-05|100000-150000?|Herman Jamke}}
+{{HistC|2005-08-24|10000-100000?|T. D. Noe}}
 {{HistF|2004-08-15|147488|Ingo Buechel,Wilfrid Keller}}
 {{HistF|2004-08-12|143552|Ingo Buechel,Wilfrid Keller}}
@@ Line 121: / Line 127: @@
 {{HistF|2001-08-12|75551|Wilfrid Keller}}
 {{HistF|2001-06-30|49340|Wilfrid Keller}}
-{{HistF|1972-10|1 - 222|Hugh C. Williams,Charles R. Zarnke}}
+{{HistC|1999-12-11|326-10000?|Douglas Burke}}
+{{HistC|1972-10|1-325|Hugh C. Williams,Charles R. Zarnke}}

Difference between revisions of "Riesel prime 3 2"

Latest revision as of 06:19, 14 November 2024

Current data

Notes

History

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