## Re: [PrimeNumbers] Known pairs vs OEIS A002072

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• I m sorry, I said 227, I really meant 229! ________________________________ From: Jim White  Subject: [PrimeNumbers] Known pairs vs
Message 1 of 4 , Mar 7, 2012
I'm sorry, I said 227, I really meant 229!

________________________________
From: Jim White <mathimagics@...>
Subject: [PrimeNumbers] Known pairs vs OEIS A002072

Having said that, and assuming both A002072 and
column k=1 of your chain table are "smallest
known", I do have a new entry for p = 227, having
found this pair (S, S+1):

S = 15487655655079919751646464

This was found via a PTE match at
Q = 395684061 {0, 3, 3}, {1, 1, 4}

Thus S = Q(Q+3)^2 / 4

Jim White
Canberra

________________________________
From: Andrey Kulsha <andrey_601@...>
To: Jim White <mathimagics@...>
Sent: Wednesday, 7 March 2012, 4:29
Subject: Re: [PrimeNumbers] Re: 13-chains of consecutive smooth numbers

﻿
Any chance of a text export?
Here we are: http://www.primefan.ru/stuff/math/maxs.txt

Chain length from 6 to
16, N up to 10^13.

Best regards,

Andrey

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• ... These values are indeed the largest known (there may be larger ones). Doubt is not about smallest but about for all i m . ... For p = 229 we have
Message 2 of 4 , Mar 10, 2012
> I wonder if the largest pair list at A002072 should
> include some statement that certain values are
> "smallest known" rather than "smallest", as the
> latter assumes the values can be confirmed in
> some rigorous manner.

These values are indeed the largest known
(there may be larger ones). Doubt is not about
"smallest" but about "for all i>m".

> I do have a new entry for p = 229, having
> found this pair (S, S+1):
>
> S = 15487655655079919751646464

For p = 229 we have 5.2*sqrt(p)-7.7 = 71,
so I expect N about exp(71), which is much

Best regards,

Andrey
• This 181-smooth pair popped up in a random search:   S = 90672220863645734556839376   Factors   S   = 2^4, 3^3, 11, 23, 29, 31, 37^2, 73, 97,
Message 3 of 4 , Mar 12, 2012
This 181-smooth pair popped up in a random search:

S = 90672220863645734556839376

Factors
S   = 2^4, 3^3, 11, 23, 29, 31, 37^2, 73, 97,
139^2, 163, 167, 181
S-1 = 5^4, 13^3, 17, 19, 43, 47, 67^2, 101^2,
113^2, 173

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