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 [URL="http://mathworld.wolfram.com/Copeland-ErdosConstant.html"]here [/URL] and their is an OEIS sequence [URL="http://oeis.org/A227529"]here[/URL].

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

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

[QUOTE=rogue;416591]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[/QUOTE]

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

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

[QUOTE=rogue;416206]OEIS sequence [URL="http://oeis.org/A227529"]here[/URL].[/QUOTE]

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

[QUOTE=ericw;416708]By any chance should that be "all primes < 30,000"?

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

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.

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.

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.

[QUOTE=rogue;418113]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.[/QUOTE]

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?

[QUOTE=ericw;418613]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?[/QUOTE]

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 ?

[QUOTE=ericw;418613]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?[/QUOTE]

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.

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?