The integer made of the first 38 digits of Pi is prime.

[Yoni]

I randomly discovered that 314159 (first 6 digits of Pi) is a prime.
So I naturally started looking for other numbers with this property:



A result was found:

31415926535897932384626433832795028841

It is the biggest prime in the first 100 digits of Pi.

Within 10 minutes I had improved my script to look in the first 10000 digits of Pi:



I know, not that efficient, but it works. Currently still running. I'll report results when it finishes, probably in a few hours.

[Slaughter]

Cool I look forward to the results

[Yoni]

The results are just in:



So, looking at the first 10000 digits of Pi, the only primes found (starting with 314...) were the ones I posted about above.

I did the same with e:



I found much bigger primes in e!
The short primes I found were:

2
271
2718281
2718281828459045235360287471352662497757247093699959574966967627724076630353547594571 (85 digits)

The 1781-digit prime:

Code Select Expand

271828182845904523536028747135266249775724709369995957496696762772407663035354
759457138217852516642742746639193200305992181741359662904357290033429526059563
073813232862794349076323382988075319525101901157383418793070215408914993488416
750924476146066808226480016847741185374234544243710753907774499206955170276183
860626133138458300075204493382656029760673711320070932870912744374704723069697
720931014169283681902551510865746377211125238978442505695369677078544996996794
686445490598793163688923009879312773617821542499922957635148220826989519366803
318252886939849646510582093923982948879332036250944311730123819706841614039701
983767932068328237646480429531180232878250981945581530175671736133206981125099
618188159304169035159888851934580727386673858942287922849989208680582574927961
048419844436346324496848756023362482704197862320900216099023530436994184914631
409343173814364054625315209618369088870701676839642437814059271456354906130310
720851038375051011574770417189861068739696552126715468895703503540212340784981
933432106817012100562788023519303322474501585390473041995777709350366041699732
972508868769664035557071622684471625607988265178713419512466520103059212366771
943252786753985589448969709640975459185695638023637016211204774272283648961342
251644507818244235294863637214174023889344124796357437026375529444833799801612
549227850925778256209262264832627793338656648162772516401910590049164499828931
505660472580277863186415519565324425869829469593080191529872117255634754639644
791014590409058629849679128740687050489585867174798546677575732056812884592054
133405392200011378630094556068816674001698420558040336379537645203040243225661
352783695117788386387443966253224985065499588623428189970773327617178392803494
65014345588970719425863987727547109629537415211151368350627526023

The 2780-digit prime:

Code Select Expand

271828182845904523536028747135266249775724709369995957496696762772407663035354
759457138217852516642742746639193200305992181741359662904357290033429526059563
073813232862794349076323382988075319525101901157383418793070215408914993488416
750924476146066808226480016847741185374234544243710753907774499206955170276183
860626133138458300075204493382656029760673711320070932870912744374704723069697
720931014169283681902551510865746377211125238978442505695369677078544996996794
686445490598793163688923009879312773617821542499922957635148220826989519366803
318252886939849646510582093923982948879332036250944311730123819706841614039701
983767932068328237646480429531180232878250981945581530175671736133206981125099
618188159304169035159888851934580727386673858942287922849989208680582574927961
048419844436346324496848756023362482704197862320900216099023530436994184914631
409343173814364054625315209618369088870701676839642437814059271456354906130310
720851038375051011574770417189861068739696552126715468895703503540212340784981
933432106817012100562788023519303322474501585390473041995777709350366041699732
972508868769664035557071622684471625607988265178713419512466520103059212366771
943252786753985589448969709640975459185695638023637016211204774272283648961342
251644507818244235294863637214174023889344124796357437026375529444833799801612
549227850925778256209262264832627793338656648162772516401910590049164499828931
505660472580277863186415519565324425869829469593080191529872117255634754639644
791014590409058629849679128740687050489585867174798546677575732056812884592054
133405392200011378630094556068816674001698420558040336379537645203040243225661
352783695117788386387443966253224985065499588623428189970773327617178392803494
650143455889707194258639877275471096295374152111513683506275260232648472870392
076431005958411661205452970302364725492966693811513732275364509888903136020572
481765851180630364428123149655070475102544650117272115551948668508003685322818
315219600373562527944951582841882947876108526398139559900673764829224437528718
462457803619298197139914756448826260390338144182326251509748279877799643730899
703888677822713836057729788241256119071766394650706330452795466185509666618566
470971134447401607046262156807174818778443714369882185596709591025968620023537
185887485696522000503117343920732113908032936344797273559552773490717837934216
370120500545132638354400018632399149070547977805669785335804896690629511943247
309958765523681285904138324116072260299833053537087613893963917795745401613722
361878936526053815584158718692553860616477983402543512843961294603529133259427
949043372990857315802909586313826832914771163963370924003168945863606064584592
512699465572483918656420975268508230754425459937691704197778008536273094171016
34349076964237222943523661255725088147792231519747

The time it takes Mathematica 5 to verify that the 1781-digit number is a prime: 6 seconds.
The time it takes Mathematica 5 to verify that the 2780-digit number is a prime: 19.5 seconds.
(Processor: Pentium 4, 3GHz)

In comparison, the prime pairs used to produce RSA keys are usually less than 100 decimal digits.
Still, these two are nowhere near the biggest primes known today, which are over 6 million digits in length.

A Google search for the 85-digit e prime found this page:
http://londerings.novalis.org/wlog/index.php/E_primes
A nice list! I have proven a slightly better result than it says on this page (on the bottom, it says no other primes were found starting at position 0 of length <= 9415. I have now proven it for <= 10000.)
Check it out.

By the way, it took less time to test e than it took to test pi, because the primes in e are smaller. (They start with 2718... while the pi primes start with 3141...)

[Topaz]

I'd like that program. Send it to me? [email protected]

[Blaze]

http://www.wolfram.com/products/mathematica/index.html

Go to try Try-It link, for a 15-day trial.

[Lenny]

http://3.141592653589793238462643383279502884197169399375105820974944592.com/

Pi to 1 million decimal places.  Not sure if that will help much in the amount of time it takes to find another prime Yoni.  Do computers still use geometric series to calculate pi?