# [seqfan] Re: not all prime

Ray Chandler rayjchandler at sbcglobal.net
Tue Aug 17 16:14:51 CEST 2010

```Nice work.
Ray

> -----Original Message-----
> From: seqfan-bounces at list.seqfan.eu
> [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Douglas McNeil
> Sent: Tuesday, August 17, 2010 12:13 AM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] not all prime
>
> So one of the (almost) duplicate sequences, one which had a
> 3381 where there should have been a 4481, got me to
> wondering: how many sequences are supposed to be all primes
> but accidentally include composites because of typos or bugs?
>  Simplest way to find them was to scan for sequences which
> are mostly prime and check the exceptions.  Found a few
> problems, even after tossing away anything difficult to interpret:
> at least 37 sequences have nonprimes where there should be
> primes, and another 8 seem suspicious to me but I'm not
> entirely sure I understand the definitions.  Say I'm only
> half right or so, that makes ~40.
>
> Some are just carelessness:
>
> 161423 Primes in A161420.
> [3, 5, 7, 11, 19, 31, 39, 59, 79, 127]
> [(6, 39, False)]
>
> 104149 Largest prime < n^3.
> [7, 23, 61, 121, 211, 337, 509, 727, 997] [(3, 121, False)]
>
> Some are due to misplaced commas:
>
> 158473 Primes whose digit sum contains one or more digits of
> the same prime.
> [2, 3, 5, 7, 19, 109, 127, 137, 139, 149, 157, 163, 167, 173,
> 179, 181, 191, 193, 197 , 199, 271, 281, 2, 83, 307, 317,
> 337, 347, 367, 373, 379, 397, 419, 461, 463, 467, 4 91, 541,
> 557, 571, 613, 617, 619, 6, 31, 641, 643, 647, 661, 673, 691,
> 719, 733, 739,  743, 751] [(43, 6, False)]
>
> Some are truncation errors from entering really long numbers:
>
> 104119 Primes of the form 6^n + 23.
> [29, 59, 239, 1319, 46679, 60466199, 101559956668439,
> 170581728179578208279, 29324206
> 7884135544935936513642647623193965101079,
> 3950367887263302342052194671146614399477534
> 61347507325027807810991640951880679]
> [(9,
> 39503678872633023420521946711466143994775346134750732502780781
> 0991640951880679,
> False)]
>
> and some I can't understand at all unless the sequence was
> being computed by hand.
>
> Anyway, I'll add these to my pile of pending corrections for
> after the Wiki descends.  Bulk processing of sequences can be
> really useful, especially for low-traffic sequences..  If
> should-be-prime (or multiplicative, or additive, or whatever)
> sequences are tagged with the right Category on the Wiki then
> we can automate the verification in a much easier way, and
> dump failures to a "problem sequences" log for human
> intervention.  I can already check many formulae and
> generating functions (some errors there in my pending file),
> and though I haven't coded this yet it'd be nice to verify
> all of the intersequence relationships to look for both
> errors and missing terms that are known from another seq.
>
>
> Doug
>
> --
> Department of Earth Sciences
> University of Hong Kong
>
>
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>
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