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

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• ... 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
Message 1 of 11 , Jul 29 12:01 PM
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On Mon, 7/29/13, James Merickel <moralforce120@...> wrote:
> I am trying to add terms to http://oeis.org/A173189 , which gives the number for
> each integral base of primes obtainable by concatenating
> numbers decremented in sequence from a power of the base
> that are less than the smallest that is obtainable by
> concatenating numbers increasing in sequence from a power of
> the base.

""""
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.
"""

Why does 10000000000000100000000000011000000000000210000000000003100000000000041000000000000510000000000006100000000000071000000000000810000000000009
not yield any hits on either OEIS or google?

As it's a member of the sequence that your sequence is defined in terms of, one would expect that more primitive sequence to have been added first? Which would then enable you to simplify the horrendous description above.

Phil
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[stolen with permission from Daniel B. Cristofani]
• My little program to try to find a forward concatenation prime in base 79 tells me that no such number exists below exp(10000). Good luck finding one above
Message 2 of 11 , Jul 29 2:15 PM
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My little program to try to find a "forward concatenation prime"
in base 79 tells me that no such number exists below exp(10000).

Good luck finding one above that... ;)

By the way, I agree with Phil that the sequence of forward
concatenation primes would seem to be much more fundamental

On 7/29/2013 12:01 PM, Phil Carmody wrote:
>
> On Mon, 7/29/13, James Merickel <moralforce120@...> wrote:
>> I am trying to add terms to http://oeis.org/A173189 , which gives the number for
>> each integral base of primes obtainable by concatenating
>> numbers decremented in sequence from a power of the base
>> that are less than the smallest that is obtainable by
>> concatenating numbers increasing in sequence from a power of
>> the base.
>
> """"
> 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.
> """
>
> Why does 10000000000000100000000000011000000000000210000000000003100000000000041000000000000510000000000006100000000000071000000000000810000000000009
> not yield any hits on either OEIS or google?
>
> As it's a member of the sequence that your sequence is defined in terms of, one would expect that more primitive sequence to have been added first? Which would then enable you to simplify the horrendous description above.
>
> Phil
>
• Well, it s true that my (old) sequence is derivative of the one you describe; but a) mine is addressing the situation comparing an anomaly in base 10 as
Message 3 of 11 , Jul 30 6:16 AM
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Well, it's true that my (old) sequence is derivative of the one you describe; but a) mine is addressing the situation comparing an anomaly in base 10 as compared with others and b) I have been limited to just 3 sequences in edit at one time at OEIS--with long delays--for a while so that thoughts of completeness of my work are kind of out the window (For examples, JKA pointed out a mis-titling of an entire large collection of sequences that were edited in (where the editors failed to note an ambiguity in meaning), and I have had no really good time to fix that or to add things like palindromic primes with index differing by (small) k from palindromic).

Yes, is large, and I did not expect anybody to do this but thought I might ask. At any rate, as far as the sequence is concerned, b=79 has a very good chance of providing the 2nd largest value and possibly could overtake the value for b=10; and I appreciate any effort--successful or not--for this unusual question.

JGM
--------------------------------------------
On Mon, 7/29/13, Jack Brennen <jfb@...> wrote:

Subject: Re: [PrimeNumbers] seeking smallest 'forward concatenation prime' for power of 79
Date: Monday, July 29, 2013, 2:15 PM

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

in base 79 tells me that no such number exists below
exp(10000).

Good luck finding one above that... ;)

By the way, I agree with Phil that the sequence of forward

concatenation primes would seem to be much more fundamental

On 7/29/2013 12:01 PM, Phil Carmody wrote:

>

> On Mon, 7/29/13, James Merickel <moralforce120@...>
wrote:

>> I am trying to add terms to http://oeis.org/A173189 ,
which gives the number for

>> each integral base of primes obtainable by
concatenating

>> numbers decremented in sequence from a power of the
base

>> that are less than the smallest that is obtainable
by

>> concatenating numbers increasing in sequence from a
power of

>> the base.

>

> """"

> 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

> """

>

> Why does
10000000000000100000000000011000000000000210000000000003100000000000041000000000000510000000000006100000000000071000000000000810000000000009

> not yield any hits on either OEIS or google?

>

> As it's a member of the sequence that your sequence
is defined in terms of, one would expect that more primitive
sequence to have been added first? Which would then enable
you to simplify the horrendous description above.

>

> Phil

>
• Addressing the question of why the particular number is not in OEIS is my preceding, and why it is not googlable (?) is down to how it is recorded at Prime
Message 4 of 11 , Jul 30 6:19 AM
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Addressing the question of why the particular number is not in OEIS is my preceding, and why it is not googlable (?) is down to how it is recorded at Prime Curios! because of length (and is not elsewhere to my knowledge).
--------------------------------------------
On Mon, 7/29/13, Phil Carmody <thefatphil@...> wrote:

Subject: Re: [PrimeNumbers] seeking smallest 'forward concatenation prime' for power of 79
Date: Monday, July 29, 2013, 12:01 PM

On Mon, 7/29/13, James Merickel <moralforce120@...>
wrote:

> I am trying to add terms to http://oeis.org/A173189 ,
which gives the number for

> each integral base of primes obtainable by
concatenating

> numbers decremented in sequence from a power of the
base

> that are less than the smallest that is obtainable by

> concatenating numbers increasing in sequence from a
power of

> the base.

""""

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

"""

Why does
10000000000000100000000000011000000000000210000000000003100000000000041000000000000510000000000006100000000000071000000000000810000000000009

not yield any hits on either OEIS or google?

As it's a member of the sequence that your sequence is
defined in terms of, one would expect that more primitive
sequence to have been added first? Which would then enable
you to simplify the horrendous description above.

Phil

--

() ASCII ribbon campaign () Hopeless ribbon
campaign

/\ against HTML mail /\ against
gratuitous bloodshed

[stolen with permission from Daniel B. Cristofani]
• ... Assuming fixed irrelevant base B, the number of candidates with up to d digits is approximately N_d = Sum{l=1..d} floor(d/l) Roughly the area under the
Message 5 of 11 , Jul 30 10:08 AM
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> My little program to try to find a "forward concatenation prime"
> in base 79 tells me that no such number exists below
> exp(10000).
>
> Good luck finding one above that...  ;)

Assuming fixed irrelevant base B, the number of candidates with up to d digits is approximately
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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/\ against HTML mail /\ against gratuitous bloodshed

[stolen with permission from Daniel B. Cristofani]
• The suggestion is now submitted as A227775 (in draft). ... On Tue, 7/30/13, James Merickel wrote: Subject: Re: [PrimeNumbers] seeking
Message 6 of 11 , Jul 30 1:44 PM
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The suggestion is now submitted as A227775 (in draft).
--------------------------------------------
On Tue, 7/30/13, James Merickel <moralforce120@...> wrote:

Subject: Re: [PrimeNumbers] seeking smallest 'forward concatenation prime' for power of 79
Date: Tuesday, July 30, 2013, 6:16 AM

Well, it's true that my (old) sequence is
derivative of the one you describe; but a) mine is
addressing the situation comparing an anomaly in base 10 as
compared with others and b) I have been limited to just 3
sequences in edit at one time at OEIS--with long delays--for
a while so that thoughts of completeness of my work are kind
of out the window (For examples, JKA pointed out a
mis-titling of an entire large collection of sequences that
were edited in (where the editors failed to note an
ambiguity in meaning), and I have had no really good time to
fix that or to add things like palindromic primes with index
differing by (small) k from palindromic).

Yes, is large, and I did not expect anybody to do this but
thought I might ask. At any rate, as far as the sequence is
concerned, b=79 has a very good chance of providing the 2nd
largest value and possibly could overtake the value for
b=10; and I appreciate any effort--successful or not--for
this unusual question.

JGM

--------------------------------------------

On Mon, 7/29/13, Jack Brennen <jfb@...>
wrote:

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

Date: Monday, July 29, 2013, 2:15 PM

My little program to try to find a "forward

concatenation prime"

in base 79 tells me that no such number exists below

exp(10000).

Good luck finding one above that... ;)

By the way, I agree with Phil that the sequence of forward

concatenation primes would seem to be much more
fundamental

On 7/29/2013 12:01 PM, Phil Carmody wrote:

>

> On Mon, 7/29/13, James Merickel <moralforce120@...>

wrote:

>> I am trying to add terms to http://oeis.org/A173189
,

which gives the number for

>> each integral base of primes obtainable by

concatenating

>> numbers decremented in sequence from a power of
the

base

>> that are less than the smallest that is
obtainable

by

>> concatenating numbers increasing in sequence from
a

power of

>> the base.

>

> """"

> 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

> """

>

> Why does

10000000000000100000000000011000000000000210000000000003100000000000041000000000000510000000000006100000000000071000000000000810000000000009

> not yield any hits on either OEIS or google?

>

> As it's a member of the sequence that your
sequence

is defined in terms of, one would expect that more
primitive

sequence to have been added first? Which would then enable

you to simplify the horrendous description above.

>

> Phil

>
• ... James logorrhea is utterly baffling, to me. I am usually able to understand definitions posted on this list, even when they are obfuscated. But the
Message 7 of 11 , Jul 30 3:53 PM
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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

James' logorrhea is utterly baffling, to me.
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
• 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
Message 8 of 11 , Jul 30 5:46 PM
• 0 Attachment
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.

On 7/30/2013 3:53 PM, djbroadhurst wrote:
>
>
> 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
>
> James' logorrhea is utterly baffling, to me.
> 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
>
>
>
> ------------------------------------
>
> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
> The Prime Pages : http://primes.utm.edu/
>
>
>
>
>
>
• As noted, I have responded by submitting the suggested sequence to simplify this. I will point out that at least one OEIS editor apparently understood this.
Message 9 of 11 , Jul 31 8:53 AM
• 0 Attachment
As noted, I have responded by submitting the suggested sequence to simplify this. I will point out that at least one OEIS editor apparently understood this. The change to the title may still be long; so, David, once you've figured out what I mean perhaps you will have better wording than the obvious change being made that refers to A227775.
JGM
--------------------------------------------

Subject: [PrimeNumbers] Re: seeking smallest 'forward concatenation prime' for power of 79
Date: Tuesday, July 30, 2013, 3:53 PM

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

>

> simplify the horrendous description above

James' logorrhea is utterly baffling, to me.

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
• 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.
Message 10 of 11 , Jul 31 9:01 AM
• 0 Attachment
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
> Date: Tuesday, July 30, 2013, 5:46 PM
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> 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.
>
>
>
> On 7/30/2013 3:53 PM, djbroadhurst wrote:
>
> >
>
> >
>
>
> > 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
>
> >>
>
> >> simplify the horrendous description above
>
> >
>
> > James' logorrhea is utterly baffling, to me.
>
> > 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
>
> >
>
> >
>
> >
>
> > ------------------------------------
>
> >
>
> > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
>
> > The Prime Pages : http://primes.utm.edu/
>
> >
>
>
> >
>
> >
>
> >
>
> >
>
> >
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
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