Woodall primes and Near Woodall Primes

Latest News:

2014-07-29: new Near Woodall prime was found: 454483·21817935-1 = 1817932·21817933-1.
2012-11-14: new Near Woodall prime was found: 582833·21165668-1 = 1165666·21165667-1.
2012-10-03: new Near Woodall prime was found: 586085·21172172-1 = 1172170·21172171-1.
2010-11-17: new Near Woodall prime was found: 197673·2790695-1 = 790692·2790693-1.
2010-02-09: new Near Woodall prime was found: 665127·2665128-1.
2010-02-01: new Near Woodall prime was found: 41197·2659157-1 = 659152·2659153-1.
2009-09-11: new Near Woodall prime was found!
2008-09-25: new Near Woodall prime was found!

See reserved and checked ranges for Woodall Search here.
See the Top 5000 Top 20 Woodall Primes here.
A list of Near Woodall Primes / Near Cullen Primes can be found here.

Woodall Primes

A Woodall prime is any prime of the form n·2n-1. It is conjectured that there are infinitely many Woodall primes.

History:
1968: H.Riesel listet all Woodall Primes for n≤110
1984: W.Keller searched for n≤15000 (some Woodall Primes found by others but not listed as)
1987: W.Keller searched for n<20000

Note: The Woodall Primes for n=2 and n=512 are Mersenne Primes!

There are 33 Woodall primes discovered so far :

This table contains all Woodall Primes with n<5000000.

no.n#digitsnormalized formwho founddate
12123-1--
2323·23-1--
3633·27-1--
4301115·231-1H.Riesel1968
5752575·275-1H.Riesel1968
6812781·281-1H.Riesel1968
711537115·2115-1H.C.Williams, C.R.Zarnke1968
812340123·2123-1W.Keller1984
924978249·2249-1W.Keller1984
10362112181·2363-1I.Jönsson1972
113841193·2391-1H.Riesel1969
12462142231·2463-1W.Keller1984
135121572521-1R.M.Robinson1952-01-30
14751229751·2751-1W.Keller1984
15822251411·2823-1W.Keller1984
165312160383·25318-1W.Keller1984-12
17775523397755·27755-1W.Keller1984-12
18953128749531·29531-1W.Keller1984-12
1912379373112379·212379-1W.Keller1984-12
201582247687911·215823-1W.Keller1987-12
2118885569018885·218885-1W.Keller1987-12
2222971692022971·222971-1J.Young1997-05
2323005693023005·223005-1J.Young1997-05
24987262972549363·298727-1J.Young1997-05
251430184305871509·2143019-1R.Ballinger1998-04-25
2615102345468151023·2151023-1K.O'Hare1998-05-01
27667071200815667071·2667071-1M.Toplic2000-09-25
2811952033597991195203·21195203-1M.Rodenkirch2005-07-11
2912689793820071268979·21268979-1W.Siemelink2007-01-25
3014677634418471467763·21467763-1W.Siemelink, Z.Mate, M.Rodenkirch2007-06-07
312013992606279251749·22013995-1L.M.Andersen2007-08-09
3223679067128181183953·22367907-1S.Kohlman2007-09-03
3337529481129757938237·23752950-1M.J.Thompson2007-12-26


Near Woodall primes (form (n+1)·2n-1):

Note: The Near Woodall Primes for n=1, n=3 and n=15 are Mersenne Primes!

This table contains all Near Woodall Primes with n<1100000.
no.n#digitsnormalized formwho founddate
11122-1n.n.n.n.
2223·22-1n.n.n.n.
33225-1n.n.n.n.
4425·24-1n.n.n.n.
5533·26-1n.n.n.n.
6945·210-1n.n.n.n.
714615·214-1n.n.n.n.
8156219-1n.n.n.n.
916717·216-1n.n.n.n.
1027107·229-1n.n.n.n.
11451623·246-1n.n.n.n.
1212239123·2122-1n.n.n.n.
131254063·2126-1n.n.n.n.
1421367107·2214-1n.n.n.n.
1524276243·2242-1n.n.n.n.
1625680257·2256-1n.n.n.n.
172638233·2266-1n.n.n.n.
1829090291·2290-1n.n.n.n.
19855261107·2858-1n.n.n.n.
201059322265·21061-1n.n.n.n.
2122736881137·22274-1n.n.n.n.
22394511921973·23946-1n.n.n.n.
2339991208125·24004-1n.n.n.n.
24951228689513·29512-1H.Lifchitz1998-07-03
25141274257883·214131-1H.Lifchitz1998-07-03
2616486496716487·216486-1H.Lifchitz1998-07-03
2720056604220057·220056-1H.Lifchitz1998-07-03
2828834868528835·228834-1H.Lifchitz1998-07-03
29414931249620747·241494-1H.Lifchitz1998-07-03
301591474791439787·2159149-1R.Ballinger2000-05-19
312271396838256785·2227141-1R.Ballinger2000-07-28
3258782317695936739·2587827-1S.Harvey2009-09-11


Near Woodall primes (form (n-1)·2n-1):

Note: The Near Woodall Primes for n=2 and n=5 are Mersenne Primes!

This table contains all Near Woodall Primes with n<1100000.
no.n#digitsnormalized formwho founddate
12122-1n.n.n.n.
2423·24-1n.n.n.n.
35327-1n.n.n.n.
41155·212-1n.n.n.n.
5281027·228-1n.n.n.n.
6351317·236-1n.n.n.n.
723574117·2236-1n.n.n.n.
832510181·2327-1n.n.n.n.
9551169275·2552-1n.n.n.n.
10688210687·2688-1n.n.n.n.
11703721231759·27039-1n.n.n.n.
12889626828895·28896-1n.n.n.n.
1310020302110019·210020-1M.Oakesn.n.
141359740983399·213599-1M.Oakesn.n.
1521347643110673·221348-1H.Lifchitz1998-07-03
1611802035533118019·2118020-1S.Harvey2002-06-27
17446694134474446693·2446694-1S.Harvey2008-09-25
1865915319843141197·2659157-1S.Harvey2010-02-01
19665128200230665127·2665128-1S.Harvey2010-02-09
20790693238029197673·2790695-1S.Harvey2010-11-17
211165667350907582833·21165668-1S.Harvey2012-11-14
221172171352865586085·21172172-1S.Harvey2012-10-03
231817933547259454483·21817935-1S.Harvey2014-07-29