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 February 10th, 2010, 05:48 PM #11 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Re: An infinite number (?) of primes using the uple totient Big big thank you!!!!!!!! Can you send the prime generated too. How to send the output to a file (Pari/gp)?
 February 10th, 2010, 05:52 PM #12 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Re: An infinite number (?) of primes using the uple totient The sequence seems to be as infinite as we wish. Is that right?
February 10th, 2010, 06:10 PM   #13
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Re: An infinite number (?) of primes using the uple totient

Quote:
 Originally Posted by momo Can you send the prime generated too.
I didn't record it, but you can get the prime at any stage with phiset. So
Code:
phiset([1, 2, 2, 2, 2, 2, 3, 8, 3, 22, 2, 7, 3, 8, 10, 1, 4, 6, 4, 2, 1, 1, 7, 2, 16, 4, 1, 15, 12, 2, 10, 5, 3, 11, 3, 3, 3, 5, 5, 22, 3, 13, 6, 11, 33, 27, 16, 2, 2, 9, 5, 10, 1, 21, 5, 22, 7, 20, 12, 8, 12, 3, 10, 4, 24, 3, 8, 1, 4, 14, 13, 22, 7, 31, 24, 16, 9, 7, 6, 14, 4, 2, 6, 3, 14, 2, 9, 5, 18, 74, 23, 24, 8, 16, 3, 24, 5, 2, 4, 7, 6, 2, 1, 17, 10, 11, 29, 7, 18, 2, 16, 6, 21, 2, 10, 9, 2, 8, 6, 13, 2, 4, 9, 4, 21, 17, 5, 4, 5, 10, 3, 10, 3, 11, 5, 5, 10, 28, 1, 10, 30, 10, 8, 14, 28, 47, 6, 7, 13, 17])
gives you the 149th prime (phiset([1]) is not prime).

You could get all of the primes generated by [1,2], [1,2,2], ..., v with
Code:
for(i=2,#v,print(i" "phiset(vector(i,j,v[j]))))
Quote:
 Originally Posted by momo How to send the output to a file (Pari/gp)?
write(filename, stuff to write to file)

So if you wanted to print all members of v to a file, you could do
Code:
for(i=1,#v,write("filename.txt", v[i]))
or even
Code:
for(i=1,#v,write("filename.txt", i, " ", v[i]))
to write line numbers. You don't even need commas between the things you're writing, so I usually omit them:
Code:
for(i=1,#v,write("filename.txt", i" "v[i]))
which looks neater to me.

February 10th, 2010, 06:18 PM   #14
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Re: An infinite number (?) of primes using the uple totient

Quote:
 Originally Posted by momo The sequence seems to be as infinite as we wish. Is that right?
It seems extremely likely. For it to fail, there would be some n with
?(a1, a2, ..., an) is prime
[a1, a2, ... are your U] but for any x,
?(a1, a2, ..., an, x) is composite.

I can't think of a reason that this would happen, but I can't rule it out immediately.

 February 10th, 2010, 06:24 PM #15 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Re: An infinite number (?) of primes using the uple totient Big big thank you for all your help! Now I'm going to try to sleep. I know it is hard when a lot of ideas are boiling on my head. Good night!
 February 11th, 2010, 10:01 AM #16 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Re: An infinite number (?) of primes using the uple totient Hi, I have found a link between the uple totient ?(2,3,5,7,11,....p) and the prime counting function ?(n) I'm trying to express explicitely the link between the 2. ?(n)=F(?(2,3,5,7,11,....p)) I do not have enough data to formulate precisely the link. Any idea will be welcomed.
 June 3rd, 2017, 03:19 PM #17 Banned Camp   Joined: Dec 2013 Posts: 1,117 Thanks: 41 I`m very sad because my previous posts were damaged. Why is ? replacing phi()? In this post I developed a way to generate an infinite number of primes by using the uple-totient.

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