> My little program to try to find a "forward concatenation prime"

Assuming fixed irrelevant base B, the number of candidates with up to d digits is approximately

> in base 79 tells me that no such number exists below

> exp(10000).

>

> Good luck finding one above that... ;)

N_d = Sum{l=1..d} floor(d/l)

Roughly the area under the hyperbola xy=d, 1<x<d

Double d, and that area doubles.

i.e at each individual digit length there's on average the same number of candidates.

With density ~1/d. The sum of which diverges, so such a search isn't necessarily futile.

However, given how slowly it diverges, one shouldn't hold out too much hope, as you say.

Phil

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[stolen with permission from Daniel B. Cristofani]- I gather that Mr. Brennen meant the list to exclude powers of 10 from his remark on searching base 79, and this would be correct.

--- On Tue, 7/30/13, Jack Brennen <jfb@...> wrote:

> From: Jack Brennen <jfb@...>

> Subject: Re: [PrimeNumbers] Re: seeking smallest 'forward concatenation prime' for power of 79

> To: "djbroadhurst" <d.broadhurst@...>

> Cc: primenumbers@yahoogroups.com

> Date: Tuesday, July 30, 2013, 5:46 PM

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> I divined the "lesser problem" from the

> base 10 curiosity previously linked.

>

>

>

> Basically, take all of the positive integers that can be

> obtained

>

> by starting with a power of 10 and concatenating consecutive

> increasing

>

> numbers:

>

>

>

> 10

>

> 1011

>

> 101112

>

> 10111213

>

> 1011121314

>

> 100

>

> 100101

>

> 100101102

>

> 1000

>

> 10001001

>

> 100010011002

>

> ...

>

>

>

> The smallest such prime is the 140 digit number linked as a

> prime

>

> curio in James' first post on this subject, consisting

> of the ten

>

> consecutive numbers from 10^13 to 10^13+9 concatenated.

>

>

>

> The fundamental question to this thread is to find the

> smallest such

>

> prime when operating in base 79. I assume that the trivial

> example

>

> of 10(base 79) is excluded, although it is prime.

>

>

>

> I ended up searching up to about 6500 decimal digits without

> finding

>

> such a prime.

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>

>

> On 7/30/2013 3:53 PM, djbroadhurst wrote:

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> >

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> >

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> > --- In primenumbers@yahoogroups.com,

>

> > Phil Carmody <thefatphil@...> wrote:

>

> >

>

> >>> In base n, the number of primes beginning with

> a power of n

>

> >>> that are a concatenation of simply decremented

> numbers that

>

> >>> are less than the smallest prime that is a

> similar concatenation

>

> >>> beginning with a power of n and proceeding by

> increments instead.

>

> >>

>

> >> simplify the horrendous description above

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> >

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> > James' logorrhea is utterly baffling, to me.

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> > I am usually able to understand definitions

>

> > posted on this list, even when they are obfuscated.

>

> > But the logorrheic convolution above defeats me.

>

> > Only sharp minds, like Jack's, seem able to decode

> it.

>

> >

>

> > Please, Jack, might you give us lesser mortals some

> idea of

>

> > what you have divined from James' verbiage?

>

> >

>

> > David

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> >

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> >

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> >

>

> > ------------------------------------

>

> >

>

> > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com

>

> > The Prime Pages : http://primes.utm.edu/

>

> >

>

> > Yahoo! Groups Links

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