mersenneforum.org Find factors with k = 2^n - 1 = Mersenne prime
 User Name Remember Me? Password
 Register FAQ Search Today's Posts Mark Forums Read

 2023-05-15, 08:35 #1 Dobri   "ม้าไฟ" May 2018 10228 Posts Find factors with k = 2^n - 1 = Mersenne prime Examples: n = 2, p = 5, k = 2n - 1 = M2, 2kp + 1 = 31 = M5; n = 3, p = 929, k = 2n - 1 = M3, 2kp + 1 = 13007 is a factor of M929; n = 5, p = 1973, k = 2n - 1 = M5, 2kp + 1 = 122327 is a factor of M1973; n = 7, p = 37097, k = 2n - 1 = M7, 2kp + 1 = 9422639 is a factor of M37097; n = 13, p = 1946669, k = 2n - 1 = M13, 2kp + 1 = 31890331559 is a factor of M1946669; etc.
 2023-05-15, 09:45 #2 Dobri   "ม้าไฟ" May 2018 2·5·53 Posts Find also factors with k = 2m(2n - 1), for example: m = 7, n = 5, p = 270601, k = 27(2n - 1) = 27M5, 2kp + 1 = 2147489537 is a factor of M270601.
 2023-05-15, 09:58 #3 Dobri   "ม้าไฟ" May 2018 2×5×53 Posts Find also factors with k given as a product of Mersenne primes (not necessarily distinct ones) k = 2m(2n1 - 1)(2n2 - 1)... The challenge is to find a NEW factor.
 2023-05-17, 06:53 #4 Dobri   "ม้าไฟ" May 2018 53010 Posts Let's set an upper limit for finding NEW factors, p < 10000001113, where n = 2, p = 10000001113, k = 2n - 1 = M2, 2kp + 1 = 60000006679. The leading entry should have the biggest n value. For starters, n = 2.
 2023-05-17, 08:59 #5 Dobri   "ม้าไฟ" May 2018 2·5·53 Posts Note that if there are several entries for a given n value, the corresponding leading entry for said n is the one with the smallest p value.

 Similar Threads Thread Thread Starter Forum Replies Last Post alpertron Data 7 2021-12-28 17:32 houding PrimeNet 1 2014-02-24 20:25 devarajkandadai Miscellaneous Math 15 2012-05-29 13:18 alpertron Math 0 2006-06-23 20:07 devarajkandadai Miscellaneous Math 6 2006-01-04 22:44

All times are UTC. The time now is 13:45.

Sun May 28 13:45:22 UTC 2023 up 283 days, 11:13, 0 users, load averages: 1.47, 1.25, 1.18

Copyright ©2000 - 2023, 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