mersenneforum.org Primes in π
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2012-07-18, 04:16   #23
bsquared

"Ben"
Feb 2007

CDD16 Posts

Quote:
 Originally Posted by Dubslow I Am Not A National Treasure???
Clearly not :) but also not a Number Theorist.

 2012-07-18, 18:54 #24 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,127 Posts 98 -> 9862803482...07182848167<61303> PRP
2012-07-19, 15:02   #25
kar_bon

Mar 2006
Germany

2·1,423 Posts

Quote:
 Originally Posted by Batalov For 62, the PRP is 3490-digit. (...) (these would be easy to prove prime)
... is proven prime here.

 2012-07-19, 17:01 #26 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 100011101001112 Posts a(20) and a(96) both would be larger than 71000 digits. Running up to 100k digits.
2012-07-20, 00:38   #27
kar_bon

Mar 2006
Germany

284610 Posts

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

All needed info. are given in the attachment.
Attached Files
 PI-Primes.txt (3.6 KB, 409 views)

 2012-07-20, 01:13 #28 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,127 Posts Ah. Interesting to compare different programming styles. Here's my scriptus. Code: #!/usr/bin/perl -w $N=(shift || '20'); # Pi is prepared by gp :: \p 100000; write("Pi",Pi) open IN, "Pi";$_=; s/\s+$//;$l=length($_); for($i=0;\$i
 2012-07-23, 06:47 #29 gd_barnes     May 2007 Kansas; USA 2·36·7 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 -> (41938-digit PRP already posted) 11 --> 1170679 12 --> 1284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903` Using the restriction of disallowing the number (sequence) itself as a prime, does this affect any already calculated results for sequences > 12 ? Last fiddled with by gd_barnes on 2012-07-23 at 07:09
2012-07-23, 07:04   #30
kar_bon

Mar 2006
Germany

1011000111102 Posts

Quote:
 Originally Posted by gd_barnes Using the restriction of disallowing the number (sequence) itself as a prime, does this affect any results for sequences > 12 ?
13, 17, 19, 23, 29,... and many others (see file in post #9).

Last fiddled with by kar_bon on 2012-07-23 at 07:04

2012-07-23, 07:08   #31
gd_barnes

May 2007
Kansas; USA

2·36·7 Posts

Quote:
 Originally Posted by kar_bon 13, 17, 19, 23, 29,... and many others (see file in post #9).
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.

 2012-07-23, 07:16 #32 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,127 Posts 17 gets in a spot of trouble but it has a 6918-digit PRP. Others (I checked only a few ...up to 100... 200) escape easily. Last fiddled with by Batalov on 2012-07-23 at 07:51
 2012-08-10, 01:27 #33 davar55     May 2004 New York City 2×32×5×47 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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