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## 23571113171923... prime?

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• Let seq(p) = 23571113171923...p seq(2) = 2 = prime seq(3) = 23 = prime seq(7) = 2357 = prime Is there any p 7 for which seq(p) is prime? I tried up to p =
Message 1 of 4 , Mar 5, 2006
Let seq(p) = 23571113171923...p
seq(2) = 2 = prime
seq(3) = 23 = prime
seq(7) = 2357 = prime

Is there any p > 7 for which seq(p) is prime? I tried up to p = 223.

Werner
• ... Well, I have a small archive of posts to the group before the group was moved to yahoo, and this was brought up before, here was the highest that anyone on
Message 2 of 4 , Mar 5, 2006
"Werner D. Sand" wrote:
>
> Let seq(p) = 23571113171923...p
> seq(2) = 2 = prime
> seq(3) = 23 = prime
> seq(7) = 2357 = prime
>
> Is there any p > 7 for which seq(p) is prime? I tried up to p = 223.
>
> Werner

Well, I have a small archive of posts to the group before the group was
moved to yahoo, and this was brought up before, here was the highest
that anyone on the list (at that time) came up with:

On Mon, 24 Apr 2000 Brian Schroeder wrote:
> Well, prime_cat(2,719) is prime with 355 digits and prime_cat(2,1033) > is prime with 499 digits and prime_cat(2,2297) is prime with 1171 > digits and prime_cat(2,3037) is prime with 1543 digits.

And then we got another excelent result from Marcel Martin who wrote:

On Tue, 25 Apr 2000 Marcel Martin wrote:
> Hello all,
>
> Sorry for my last mail. I gave the same infos than Brian Schroeder.
> I received his mail after having sent mine :(
>
> Well, I let my PC run all day long. All numbers from > prime_cat(2,3041) to prime_cat(2,11923) are composite.
>
> prime_cat(2,11927) is a strong pseudoprime for the bases 2, 3, 5,
> 7 and 11. This number has 5719 decimal digits.
>
> Marcel Martin

Where we defined prime_cat(x,y) to be the concatenation of all primes
from x to y, inclusively. I'd be curious to know, has anyone done any
more work on this since then?

-David C.
• ... http://mathworld.wolfram.com/ConsecutiveNumberSequences.html says Eric Weisstein found no other prp s in the first 14897 terms. prime(14897) = 162623 gives
Message 3 of 4 , Mar 5, 2006
David Cleaver wrote:
> I'd be curious to know, has anyone done any
> more work on this since then?

http://mathworld.wolfram.com/ConsecutiveNumberSequences.html says
Eric Weisstein found no other prp's in the first 14897 terms.
prime(14897) = 162623 gives a number with 78364 digits.

--
Jens Kruse Andersen
• Thanks for answers! Werner
Message 4 of 4 , Mar 6, 2006