mersenneforum.org M31 216091
 User Name Remember Me? Password
 Register FAQ Search Today's Posts Mark Forums Read

 2005-06-24, 10:22 #12 thommy   1216 Posts Why are those primes general Mersennes? What is your definition of it?
2005-06-24, 18:30   #13
TTn

2·3·7·17 Posts
definition

Official definition:

Quote:
 Let t(x) be the highest power of 2 which divides x+1. Then a(1)=3; a(n) is the least prime p for which t(p) > t(a(n-1)).

Quote:
 An easier way to look at them is by listing Riesel primes (k<2^n), in order of their size(digits), R=3 7 11 23 31 47 79 127 191 223 239 383 479 607 863 1087 1151 1279... n=2 3 2 3 5 4 4 7 6 5 4 7 5 5 5 6 7 8 ...
As you can see, Mersenne primes by default, always have the largest exponent n, up that particular point. So what about the others?
The procedure for the algorithm is to, "reduce to lowest terms".
Since ie, 1*2^7-1 is also equal to, 2*2^6-1, 4*2^5-1,
8*2^4-1, 16*2^3-1, 32*2^2-1, 64*2^1-1, and 128*2^0-1. The lowest term, of the multiplier(k), reveals a prime exponent(n) with Mersenne primes.

 2005-06-27, 18:44 #14 TTn   5·1,597 Posts update 61051 216113 is prime! Update of the contiguous sequence: 1 216091-1 62431 216093-1 97065 216095-1 16371 216098-1 55847 216100-1 48609 216101-1 22311 216103-1 6213 216107-1 20265 216109-1 74697 216110-1 122649 216111-1 61051 216113-1
 2005-07-13, 08:46 #15 TTn   173C16 Posts There seems to be a large gap between primes here. I have passed k=500,000 with n=216113. It should hit one soon, and keep the average at about one prime per week.
 2005-07-15, 13:31 #16 TTn   10100100111102 Posts I just noticed the strangest thing, ... when I opened up this forum, It loaded as if it were back 2004. I saw old messages about networked LLR, and moderators needed. Anyways, a new prime! 287453 216114 Update: 1 216091-1 62431 216093-1 97065 216095-1 16371 216098-1 55847 216100-1 48609 216101-1 22311 216103-1 6213 216107-1 20265 216109-1 74697 216110-1 122649 216111-1 61051 216113-1 287453 216114-1
 2005-07-19, 00:02 #17 TTn   32·5·101 Posts Update: 1 216091-1 62431 216093-1 97065 216095-1 16371 216098-1 55847 216100-1 5/11/05 48609 216101-1 22311 216103-1 6213 216107-1 20265 216109-1 74697 216110-1 122649 216111-1 61051 216113-1 287453 216114-1 185551 216115-1 7/18/05 New!

All times are UTC. The time now is 18:31.

Thu Aug 11 18:31:04 UTC 2022 up 35 days, 13:18, 3 users, load averages: 1.25, 1.21, 1.25

Copyright ©2000 - 2022, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔