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-   -   Primes in π (https://www.mersenneforum.org/showthread.php?t=16978)

 bsquared 2012-07-18 04:16

[QUOTE=Dubslow;305072]I Am Not A National Treasure???[/QUOTE]

Clearly not :) but also not a Number Theorist.

 Batalov 2012-07-18 18:54

98 -> 9862803482...07182848167[SUB]<61303>[/SUB] PRP

 kar_bon 2012-07-19 15:02

[QUOTE=Batalov;304950]For 62, the PRP is 3490-digit.
(...)
(these would be easy to prove prime)[/QUOTE]

... is proven prime [url=http://factordb.com/index.php?id=1100000000524129946]here[/url].

 Batalov 2012-07-19 17:01

a(20) and a(96) both would be larger than 71000 digits. Running up to 100k digits.

 kar_bon 2012-07-20 00:38

1 Attachment(s)
Here's some code for finding possible numbers of PI-digit-primes for testing with pfgw.

All needed info. are given in the attachment.

 Batalov 2012-07-20 01:13

Ah. Interesting to compare different programming styles.
Here's my scriptus.
[CODE]#!/usr/bin/perl -w
\$N=(shift || '20');
# Pi is prepared by gp :: \p 100000; write("Pi",Pi)
open IN, "Pi";
\$_=<IN>;
s/\s+\$//;
\$l=length(\$_);
for(\$i=0;\$i<length(\$_) && (substr(\$_,\$i,length(\$N)) ne \$N);\$i++) {}
die unless substr(\$_,\$i,length(\$N)) eq \$N;
\$s3=substr(\$_,\$i,1); # sum of digits for divisibilty-by-3 test
for(\$j=1;\$j<\$l-\$i;\$j++) {
\$s3+=substr(\$_,\$i+\$j,1);
print substr(\$_,\$i,\$j+1),"\n" if(substr(\$_,\$i+\$j,1) =~ /[1379]/ && \$s3%3!=0);
}
#then run pfgw -f cfile
[/CODE]

 gd_barnes 2012-07-23 06:47

IMHO, it makes some of the sequences "uninteresting" if we allow the number itself as a prime. To make them more interesting, I think that only primes with digits added should be allowed. Doing this, we have the following smallest primes from the 1st post of this thread:

[code]
1 --> 14159
2 --> 26535897932384626433832795028841971693993751058209
3 --> 31
4 --> 41
5 --> 59
6 --> 653
7 --> 79
8 --> 89
9 --> 9265358979323
10 -> (41938-digit PRP already posted)
11 --> 1170679
12 --> 1284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903
[/code]

Using the restriction of disallowing the number (sequence) itself as a prime, does this affect any already calculated results for sequences > 12 ?

 kar_bon 2012-07-23 07:04

[QUOTE=gd_barnes;305563]Using the restriction of disallowing the number (sequence) itself as a prime, does this affect any results for sequences > 12 ?[/QUOTE]

13, 17, 19, 23, 29,... and many others (see file in post #9).

 gd_barnes 2012-07-23 07:08

[QUOTE=kar_bon;305565]13, 17, 19, 23, 29,... and many others (see file in post #9).[/QUOTE]

Ah very good. Based on that, I would pose it as an additional difficulty to the problem to find primes with digits added to the 2-digit prime sequences.

 Batalov 2012-07-23 07:16

17 gets in a spot of trouble [SPOILER]but it has a 6918-digit PRP[/SPOILER]. Others (I checked only a few ...up to 100... 200) escape easily.

 davar55 2012-08-10 01:27

Based on the OP looking for certain primes among the digits of pi,
where is the first occurrence of each successive prime in pi,
i.e. the first "2", ... , the first "97", etc. up to say 100000.
Indexing could begin with the 3 as 1 or 0.

There are repetitions and the sequence is not in numerical order.
(I have not computed this sequence.)

Also, where are the first occurrences of the Mersenne prime exponents.
(The 8 digit ones may be far to find.)

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