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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  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: An infinite number (?) of primes using the uple totient Quote:
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]) 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:
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])) Code: for(i=1,#v,write("filename.txt", i, " ", v[i])) Code: for(i=1,#v,write("filename.txt", i" "v[i]))  
February 10th, 2010, 06:18 PM  #14  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: An infinite number (?) of primes using the uple totient Quote:
?(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 upletotient. 

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infinite, number, primes, totient, uple 
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