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2012-07-18, 04:16   #23
bsquared

"Ben"
Feb 2007

3,361 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 59·157 Posts 98 -> 9862803482...07182848167<61303> PRP
2012-07-19, 15:02   #25
kar_bon

Mar 2006
Germany

2·1,433 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 242F16 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

2·1,433 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, 472 views)

 2012-07-20, 01:13 #28 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 59·157 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 7×13×113 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

2·1,433 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

1028310 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 59×157 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 23·232 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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