20120718, 04:16  #23 
"Ben"
Feb 2007
2·1,789 Posts 

20120718, 18:54  #24 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·4,787 Posts 
98 > 9862803482...07182848167_{<61303>} PRP

20120719, 17:01  #26 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·4,787 Posts 
a(20) and a(96) both would be larger than 71000 digits. Running up to 100k digits.

20120720, 00:38  #27 
Mar 2006
Germany
3^{2}·5^{2}·13 Posts 
Here's some code for finding possible numbers of PIdigitprimes for testing with pfgw.
All needed info. are given in the attachment. 
20120720, 01:13  #28 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
22546_{8} Posts 
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; $s3=substr($_,$i,1); # sum of digits for divisibiltyby3 test for($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 
20120723, 06:47  #29 
May 2007
Kansas; USA
10525_{10} Posts 
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 > (41938digit PRP already posted) 11 > 1170679 12 > 1284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903 Last fiddled with by gd_barnes on 20120723 at 07:09 
20120723, 07:04  #30 
Mar 2006
Germany
B6D_{16} Posts 
13, 17, 19, 23, 29,... and many others (see file in post #9).
Last fiddled with by kar_bon on 20120723 at 07:04 
20120723, 07:08  #31 
May 2007
Kansas; USA
24435_{8} Posts 

20120723, 07:16  #32 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·4,787 Posts 
17 gets in a spot of trouble but it has a 6918digit PRP. Others (I checked only a few ...up to 100... 200) escape easily.
Last fiddled with by Batalov on 20120723 at 07:51 
20120810, 01:27  #33 
May 2004
New York City
5×7×11^{2} Posts 
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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