mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > Factoring

Reply
 
Thread Tools
Old 2006-07-29, 14:39   #1
ATH
Einyen
 
ATH's Avatar
 
Dec 2003
Denmark

2·52·67 Posts
Default 10^147+19

10^147+19 =

11210754325987903848222358333498946062147584250342963305961590952868977237 *
89200063699717094086741570686240243731188867201010229921060666406453209287
(both primes according to primo)

and since 10^147+1 to 10^147+17 have these factors:

10^147+1: 7
10^147+3: 17
10^147+5: 3
10^147+7: 19
10^147+9: 27779
10^147+11: 3
10^147+13: 421
10^147+15: 5
10^147+17: 3

it should be the smallest 148-digit brilliant number?

Here is all the smallest factors of the numbers up to 10^147+1229: 10^147+x.txt

Last fiddled with by ATH on 2006-07-29 at 14:41
ATH is online now   Reply With Quote
Old 2006-07-29, 15:22   #2
Kosmaj
 
Kosmaj's Avatar
 
Nov 2003

2×1,811 Posts
Default

Amazing! With such a small addition. Congratulations.

A previous interesting case is 10^77+3.

BTW, since you factored all between 10^147+19 and 10^147+1231 I guess you did that by ecm and you basically found the brilliant number on your first snfs attempt?
Kosmaj is offline   Reply With Quote
Old 2006-07-29, 16:00   #3
ATH
Einyen
 
ATH's Avatar
 
Dec 2003
Denmark

2·52·67 Posts
Default

Yes, only a few ecm factors most of which turned out to be unnecessary and then snfs on 19. I never tried any gnfs or snfs before, so I had to figure out how to use ggnfs, it took awhile.
ATH is online now   Reply With Quote
Old 2006-08-06, 07:46   #4
Andi47
 
Andi47's Avatar
 
Oct 2004
Austria

2×17×73 Posts
Default

Quote:
Originally Posted by Kosmaj
A previous interesting case is 10^77+3.
it has a factor: P39=185554311496620532371770351611143673123
Prime cofactor: P39=538925768921415130739706333069119686561

Edit: Ooops, sorry, seems I have misinterpreted Cosmaj's Line. It has already been factored here.

Last fiddled with by Andi47 on 2006-08-06 at 07:53
Andi47 is offline   Reply With Quote
Old 2006-08-07, 05:58   #5
Kosmaj
 
Kosmaj's Avatar
 
Nov 2003

2·1,811 Posts
Default

Sorry, what I wanted to say is that 10^77+3 is another known and already factored case. Fortunately it's a small one so it didn't cost you a lot of your cpu time (less than 10 minutes by msieve?).

BTW, my name is Kosmaj, pronounced "Cossmai".
Thanks.
Kosmaj is offline   Reply With Quote
Reply

Thread Tools


All times are UTC. The time now is 09:31.


Sat Aug 13 09:31:32 UTC 2022 up 37 days, 4:18, 2 users, load averages: 1.10, 1.17, 1.16

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