24117Re: 13-chains of consecutive smooth numbers

Expand Messages
• Mar 5, 2012
Andrey's chain puzzle is interesting.  Could it be
he already has found the maximum possible result
for chain length 13?

It's hard to see how that result can be beaten.

Some results with weights of 2.2 or more:

28246112570058, weight = 2.2053 (P =  1257251)
18911412089528, weight = 2.2077 (P =  1032307)
218381019281507, weight = 2.2410 (P =  2504167)
9288363679368, weight = 2.2480 (P =   587149)
3393509932556102, weight = 2.2536 (P =  7788997)
4532039198639948, weight = 2.2536 (P =  8856259)
4532039198639949, weight = 2.2536 (P =  8856259)
12469670986534198, weight = 2.2547 (P = 13762769)
10160468895884110, weight = 2.2592 (P = 12163843)
461881571558141, weight = 2.2615 (P =  3050603)
7909529450841510, weight = 2.2621 (P = 10669823)
211814723372355, weight = 2.2918 (P =  1782043)
430753934627814, weight = 2.4217 (P =  1103933)

Perhaps the 14-chain at N = 4532039198639948 might
be a good result? What are the best known results
for 14 or longer chains?

________________________________
From: Andrey Kulsha <Andrey_601@...>
Sent: Sunday, 4 March 2012, 9:53
Subject: Re: [PrimeNumbers] Two large consecutive smooth numbers

> Puzzle: find a chain of 13 consecutive p-smooth integers,
> starting at N, with log(N)/log(p) greater than
>
> log(8559986129664)/log(58393) = 2.71328

Best regards,

Andrey

[Non-text portions of this message have been removed]
• Show all 17 messages in this topic