mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math

Reply
 
Thread Tools
Old 2017-07-22, 09:08   #1
a nicol
 
Nov 2016

29 Posts
Default Do 2^p-1 numbers ever have the same first prime factor?

Looking at the small sample from http://oeis.org/A136030 - Smallest prime factor of composite Mersenne numbers:

[23, 47, 233, 223, 13367, 431, 2351, 6361, 179951, 193707721, 228479, 439, 2687, 167, 11447, 7432339208719, 2550183799, 745988807, 3391, 263, 32032215596496435569, 5625767248687, 86656268566282183151, 18121, 852133201, 150287, 2349023, 730753, 359, 43441, 383]

There are no duplicates here, but I have not checked further.

I tried looking on http://factordb.com/ but I can't work out how to get it to only list the factors of 2^p-1 numbers - I couldn't exclude non prime odd exponents.

Are there any examples of shared first prime factors?
a nicol is offline   Reply With Quote
Old 2017-07-22, 11:20   #2
science_man_88
 
science_man_88's Avatar
 
"Forget I exist"
Jul 2009
Dumbassville

839010 Posts
Default

Quote:
Originally Posted by a nicol View Post
Looking at the small sample from http://oeis.org/A136030 - Smallest prime factor of composite Mersenne numbers:

[23, 47, 233, 223, 13367, 431, 2351, 6361, 179951, 193707721, 228479, 439, 2687, 167, 11447, 7432339208719, 2550183799, 745988807, 3391, 263, 32032215596496435569, 5625767248687, 86656268566282183151, 18121, 852133201, 150287, 2349023, 730753, 359, 43441, 383]

There are no duplicates here, but I have not checked further.

I tried looking on http://factordb.com/ but I can't work out how to get it to only list the factors of 2^p-1 numbers - I couldn't exclude non prime odd exponents.

Are there any examples of shared first prime factors?
any coprime exponents can't share any factor.
science_man_88 is offline   Reply With Quote
Old 2017-07-22, 11:26   #3
a nicol
 
Nov 2016

29 Posts
Default

Quote:
Originally Posted by science_man_88 View Post
any coprime exponents can't share any factor.
Thank you!
a nicol is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
NFSNET to factor my own numbers? skan NFSNET Discussion 5 2012-11-03 16:01
Can two Mersenne numbers share a factor? James Heinrich Math 57 2011-09-12 14:16
3-factor Carmichael numbers devarajkandadai Math 4 2008-12-06 04:16
Post the numbers you have tried to factor here hyh1048576 Factoring 11 2003-12-01 07:37
Using Motorola 7410s to factor numbers or test for primality nukemyrman Hardware 7 2003-03-04 16:08

All times are UTC. The time now is 02:58.


Thu Aug 11 02:58:57 UTC 2022 up 34 days, 21:46, 2 users, load averages: 1.38, 1.14, 1.10

Powered by vBulletin® Version 3.8.11
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