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

Clearly not :) but also not a Number Theorist.

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

[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].

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

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

All needed info. are given in the attachment.

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]

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 ?

[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).

[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.

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.

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.)