Copeland-Erdos Constant Primes

rogue · 2015-11-14, 19:40

Starting with the Smaradache-Wellin sieve, it was relatively easy to turn that into a Copeland-Erdos Constant sieve. You can learn more about them here and their is an OEIS sequence here.

I've also added an CE() function to pfgw to support this.

rogue · 2015-11-18, 23:37

I have tested up to about CE(150000) which concatenates all primes < 300000. By CE(xx), I mean the Copland-Erdos constant with a length of xx. Nothing new found and continuing

ericw · 2015-11-20, 14:01

Quote:

Originally Posted by rogue

I have tested up to about CE(150000) which concatenates all primes < 300000. By CE(xx), I mean the Copland-Erdos constant with a length of xx. Nothing new found and continuing

By any chance should that be "all primes < 30,000"?

In[6]:= Total[IntegerLength[Prime[Range[30000]]]]
Out[6]= 168982

ericw · 2015-11-20, 14:02

Quote:

Originally Posted by rogue

OEIS sequence here.

(FWIW, https://oeis.org/A227530 gives the decimal digit lengths of Copland-Erdos constant primes.)

rogue · 2015-11-20, 18:01

Quote:

Originally Posted by ericw

By any chance should that be "all primes < 30,000"?

In[6]:= Total[IntegerLength[Prime[Range[30000]]]]
Out[6]= 168982

You are comparing apples to oranges. You counted the length of the concatenation of the first 30,000 primes. I was referring to all primes < 300,000, which is less than 30,000 primes.

rogue · 2015-11-24, 14:27

Completed testing all primes < 420000. This covers all Copeland-Erdos numbers in the sequence up to 200,000 decimal digits. No new PRPs and I'm still searching.

rogue · 2015-12-03, 13:44

Completed testing all primes < 550000. This covers all Copeland-Erdos numbers in the sequence up to 264,000 decimal digits. No new PRPs and I'm still searching.

ericw · 2015-12-08, 14:54

Quote:

Originally Posted by rogue

Completed testing all primes < 550000. This covers all Copeland-Erdos numbers in the sequence up to 264,000 decimal digits. No new PRPs and I'm still searching.

Thanks for posting these updates Mark. Unfortunately, I am still having a problem understanding your limits. Concatenating all primes < 550,000 gives an integer with

In[4]:= Total[IntegerLength /@ Prime[Range[PrimePi[550000]]]]
Out[4]= 260914

decimal digits. Which is close but smaller than "up to 264,000". What am I missing?

science_man_88 · 2015-12-08, 15:07

Quote:

Originally Posted by ericw

Thanks for posting these updates Mark. Unfortunately, I am still having a problem understanding your limits. Concatenating all primes < 550,000 gives an integer with

In[4]:= Total[IntegerLength /@ Prime[Range[PrimePi[550000]]]]
Out[4]= 260914

decimal digits. Which is close but smaller than "up to 264,000". What am I missing?

my thought would be ( partially form experimenting to see where it passes 264000 digits is that all 514 primes in between allow the string to be composite ?

rogue · 2015-12-09, 02:10

Quote:

Originally Posted by ericw

Thanks for posting these updates Mark. Unfortunately, I am still having a problem understanding your limits. Concatenating all primes < 550,000 gives an integer with

In[4]:= Total[IntegerLength /@ Prime[Range[PrimePi[550000]]]]
Out[4]= 260914

decimal digits. Which is close but smaller than "up to 264,000". What am I missing?

I was rounding down. I'll be more precise in my next update, but I just want to be clear that the numbers I am giving are inclusive in the sense that there are no incomplete tests below those values and some complete tests above those values.

rogue · 2015-12-11, 23:44

If I've written my code correctly then CE(292447) is PRP. Even if my code isn't correct, it is a fairly large PRP. Could someone please independently verify?

2015-11-14, 19:40	#1
rogue "Mark" Apr 2003 Between here and the 14313₈ Posts	Copeland-Erdos Constant Primes Starting with the Smaradache-Wellin sieve, it was relatively easy to turn that into a Copeland-Erdos Constant sieve. You can learn more about them here and their is an OEIS sequence here. I've also added an CE() function to pfgw to support this. Last fiddled with by rogue on 2015-11-14 at 19:41

2015-11-18, 23:37	#2
rogue "Mark" Apr 2003 Between here and the 11·577 Posts	I have tested up to about CE(150000) which concatenates all primes < 300000. By CE(xx), I mean the Copland-Erdos constant with a length of xx. Nothing new found and continuing Last fiddled with by rogue on 2015-11-18 at 23:37

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2015-11-24, 14:27	#6
rogue "Mark" Apr 2003 Between here and the 11·577 Posts	Completed testing all primes < 420000. This covers all Copeland-Erdos numbers in the sequence up to 200,000 decimal digits. No new PRPs and I'm still searching.

2015-12-03, 13:44	#7
rogue "Mark" Apr 2003 Between here and the 11×577 Posts	Completed testing all primes < 550000. This covers all Copeland-Erdos numbers in the sequence up to 264,000 decimal digits. No new PRPs and I'm still searching.

2015-12-11, 23:44	#11
rogue "Mark" Apr 2003 Between here and the 11×577 Posts	If I've written my code correctly then CE(292447) is PRP. Even if my code isn't correct, it is a fairly large PRP. Could someone please independently verify?