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Difference between revisions of "Riesel prime 2 1"

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(updates & add Woodall reference)
 
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{{Last update|2019-03-26}}
 
 
{{Riesel prime
 
{{Riesel prime
 
|Rk=1
 
|Rk=1
 +
|Rb=2
 +
|RCount=52
 
|RNash=925
 
|RNash=925
−
|RMaxn={{Num|83000000}}
+
|RMaxn=124817431
−
|RDate=2019-03-26
+
|RDate=2024-10-31
 
|RReserved=GIMPS
 
|RReserved=GIMPS
 
|RNlist=
 
|RNlist=
−
2;T:ST;C:'''[[M1]]''', Near Woodall: (1+1)*2^1-1, also (2-1)*2^2-1
+
2;T:ST;C:'''[[M1]]''', {{NWo|+|1}}, {{NWo|-|2}}, {{NWo|4|1}}
−
3;T:SW;C:'''[[M2]]''', Woodall: 2*2^2-1
+
3;T:W;C:'''[[M2]]''', {{NWo|2}}, {{NWo|8|1}}
−
5;C:'''[[M3]]''', Near Woodall: (3+1)*2^3-1
+
5;C:'''[[M3]]''', {{NWo|+|3}}, {{NWo|4|2}}, {{NWo|32|1}}
−
7;C:'''[[M4]]''', Near Woodall: (5-1)*2^5-1
+
7;C:'''[[M4]]''', {{NWo|-|5}}, {{NWo|8|2}}, {{NWo|128|1}}
−
13;C:'''[[M5]]'''
+
13;C:'''[[M5]]''', {{NWo|64|2}}, {{NWo|8192|1}}
−
17;C:'''[[M6]]'''
+
17;C:'''[[M6]]''', {{NWo|256|2}}, {{NWo|131072|1}}
−
19;C:'''[[M7]]''', Near Woodall: (15+1)*2^15-1
+
19;C:'''[[M7]]''', {{NWo|+|15}}, {{NWo|512|2}}, {{NWo|4|8}}, {{NWo|512|2}}, {{NWo|524288|1}}
−
31;C:'''[[M8]]'''
+
31;C:'''[[M8]]''', {{NWo|32768|2}}
 
61;C:'''[[M9]]'''
 
61;C:'''[[M9]]'''
 
89;C:'''[[M10]]'''
 
89;C:'''[[M10]]'''
−
107;C:'''[[M11]]'''
+
107;C:'''[[M11]]''', {{NWo|8192|8}}
 
127;C:'''[[M12]]'''
 
127;C:'''[[M12]]'''
−
521;T:W;C:'''[[M13]]''', Woodall: 512*2^512-1
+
521;T:W;C:'''[[M13]]''', {{NWo|512}}
 
607;C:'''[[M14]]'''
 
607;C:'''[[M14]]'''
 
1279;C:'''[[M15]]'''
 
1279;C:'''[[M15]]'''
Line 58: Line 59:
 
77232917;124104;C:'''[[M50]]'''
 
77232917;124104;C:'''[[M50]]'''
 
82589933;125874;C:'''[[M51]]'''
 
82589933;125874;C:'''[[M51]]'''
−
|RRemarks=For this ''k''-value these are the [[Mersenne prime]]s. All exponents ''n''<{{Num|46600000}} have been [https://www.mersenne.org/report_milestones/ verified].
+
136279841;138668;C:'''[[M52]]'''
 +
|RRemarks=For this {{Vk}}-value these are the [[Mersenne prime]]s. All exponents {{Vn}} < {{Num|70202087}} have been [https://www.mersenne.org/report_milestones/ verified].<br>The {{OEIS|l|A000043}}<br>See also {{NWi|MM|2|n}}
 
}}
 
}}
 
==See also==
 
==See also==
 
*[[Great Internet Mersenne Prime Search]]
 
*[[Great Internet Mersenne Prime Search]]
 
*[[List of known Mersenne primes]]
 
*[[List of known Mersenne primes]]
−
[[Category:Riesel prime|#.....00001]]
 

Latest revision as of 02:04, 1 November 2024

Reserved! This sequence is currently reserved by: GIMPS

Current data

k , b : 1 , 2
Type : Low
Count : 52
Nash : 925
Max n : 124,817,431
Date : 2024-10-31
Reserved : GIMPSGIMPS/Reserved
2[1], 3[2], 5[3], 7[4], 13[5], 17[6], 19[7], 31[8], 61[9], 89[10], 107[11], 127[12], 521[13], 607[14], 1279[15], 2203[16], 2281[17], 3217[18], 4253[19], 4423[20], 9689[21], 9941[22], 11213[23], 19937[24], 21701[25], 23209[26], 44497[27], 86243[28], 110503[29], 132049[30], 216091[31], 756839[32], 859433[33], 1257787[34], 1398269[35], 2976221[36], 3021377[37], 6972593[38], 13466917[39], 20996011[40], 24036583[41], 25964951[42], 30402457[43], 32582657[44], 37156667[45], 42643801[46], 43112609[47], 57885161[48], 74207281[49], 77232917[50], 82589933[51], 136279841[52]
Remarks :
For this k-value these are the Mersenne primes. All exponents n < 70,202,087 have been verified.
The sequence A000043 in OEIS
See also Williams 2n-1

Notes

  1. ↑ Sophie Germain n=2, Twin n=2, M1, Near Woodall 2•21-1, Near Woodall 1•22-1, Woodall 41-1
  2. ↑ Woodall, M2, Woodall 2•22-1, Woodall 81-1
  3. ↑ M3, Near Woodall 4•23-1, Woodall 2•42-1, Woodall 321-1
  4. ↑ M4, Near Woodall 4•25-1, Woodall 2•82-1, Woodall 1281-1
  5. ↑ M5, Woodall 2•642-1, Woodall 81921-1
  6. ↑ M6, Woodall 2•2562-1, Woodall 1310721-1
  7. ↑ M7, Near Woodall 16•215-1, Woodall 2•5122-1, Woodall 8•48-1, Woodall 2•5122-1, Woodall 5242881-1
  8. ↑ M8, Woodall 2•327682-1
  9. ↑ M9
  10. ↑ M10
  11. ↑ M11, Woodall 8•81928-1
  12. ↑ M12
  13. ↑ Woodall, M13, Woodall 512•2512-1
  14. ↑ M14
  15. ↑ M15
  16. ↑ M16
  17. ↑ M17
  18. ↑ M18
  19. ↑ M19
  20. ↑ M20
  21. ↑ M21
  22. ↑ M22
  23. ↑ M23
  24. ↑ M24
  25. ↑ M25
  26. ↑ M26
  27. ↑ M27
  28. ↑ M28
  29. ↑ M29
  30. ↑ M30
  31. ↑ M31
  32. ↑ M32
  33. ↑ M33
  34. ↑ M34
  35. ↑ M35
  36. ↑ M36
  37. ↑ M37
  38. ↑ M38
  39. ↑ M39
  40. ↑ M40
  41. ↑ M41
  42. ↑ M42
  43. ↑ M43
  44. ↑ M44
  45. ↑ M45
  46. ↑ M46
  47. ↑ M47
  48. ↑ M48
  49. ↑ M49
  50. ↑ M50
  51. ↑ M51
  52. ↑ M52

See also

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