Primes in π - Page 3

bsquared · 2012-07-18, 04:16

Quote:

Originally Posted by Dubslow

I Am Not A National Treasure???

Clearly not :) but also not a Number Theorist.

Batalov · 2012-07-18, 18:54

98 -> 9862803482...07182848167_<61303> PRP

kar_bon · 2012-07-19, 15:02

Quote:

Originally Posted by Batalov

For 62, the PRP is 3490-digit.
(...)
(these would be easy to prove prime)

... is proven prime here.

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

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

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

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:

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).

gd_barnes · 2012-07-23, 07:08

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.

Batalov · 2012-07-23, 07:16

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.

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.)

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, 07:16	#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

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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, 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.

2012-08-10, 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.)