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 February 10th, 2010, 02:39 PM #1 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 An infinite number (?) of primes using the uple totient Hi, I discovered a way to generate (maybe) an infinite number of primes using the uple totient.(read this topic viewtopic.php?f=40&t=12181 ) Let the sequence U(n)={1,2,3,1,6,2,2,4,8,3,1,13,5...} If we begin by the 2 numbers of the sequence and then we add each time the number following we will obtain a sequence of primes : double totient ?(1,2)=5 (is prime) 3-uple totient ?(1,2,3)=13 (is prime) 4-uple totient ?(1,2,3,1)=23 (is prime) 5-ulpe totient ?(1,2,3,1,6)=47 (is prime) 6-uple totient ?(1,2,3,1,6,2)=61 (is prime) and so on ?(1,2,3,1,6,2,2)=79 ?(1,2,3,1,6,2,2,4)=107 ?(1,2,3,1,6,2,2,4, =163 ?(1,2,3,1,6,2,2,4,8,3)=199 ?(1,2,3,1,6,2,2,4,8,3,1)=233 ?(1,2,3,1,6,2,2,4,8,3,1,13)=373 ?(1,2,3,1,6,2,2,4,8,3,1,13,5)=457 I have built the first 12 numbers. Can someone continue the sequence. If we have a huge sequence maybe some pattern or property will be discovered. Thank you for any help. February 10th, 2010, 03:19 PM #2 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Re: An infinite number (?) of primes using the uple totient Here is the continuation of U(n) 1,2,3,1,6,2,2,4,8,3,1,13,5,3,29,14,7,3,29,13,3,13, 39,3,22,2,3,2.... The sequence of prime generated : 5 13 23 47 61 79 107 163 199 233 373 457 491 541 563 607 641 691 739 773 821 853 887 911 937 971 997 I think that the sequence of primes is as infinite as U(n). February 10th, 2010, 04:40 PM #3 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 What is U(n)? February 10th, 2010, 04:49 PM   #4
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Re: An infinite number (?) of primes using the uple totient

Quote:
 Originally Posted by CRGreathouse What is U(n)?
U(n) is a sequence created on the basis of an algo very simple

We begin by ?(1,x)
We replace x by a number starting each time by 1
So we find 2 ---> ?(1,2) is equal to 5 (prime number)
Then we continue ?(1,2,x)
We find 3 ---> ?(1,2,3) = 13 (prime)
and so on ....

Once we have a big sequence U(n) then we can try to explain why to find some pattern and so on February 10th, 2010, 04:51 PM #5 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Re: An infinite number (?) of primes using the uple totient Here is the last one : U(n)=1,2,3,1,6,2,2,4,8,3,1,13,5,3,29,14,7,3,29,13, 3,13,39,3,22,2,3,2,3,39,3,2,13,14,7.... If you look at it some numbers are repeated February 10th, 2010, 05:04 PM   #6
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Re: An infinite number (?) of primes using the uple totient

Here is a diagramme of the prime generated :

[attachment=0:1e4wh9yc]primegnertotient.GIF[/attachment:1e4wh9yc]

What do you think about it?
Attached Images primegnertotient.GIF (6.8 KB, 374 views) February 10th, 2010, 05:18 PM   #7
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Re: An infinite number (?) of primes using the uple totient

Quote:
 Originally Posted by momo We begin by ?(1,x) We replace x by a number starting each time by 1 So we find 2 ---> ?(1,2) is equal to 5 (prime number) Then we continue ?(1,2,x) We find 3 ---> ?(1,2,3) = 13 (prime) and so on ....
Why 3? ?(1, 2, 2) = 11 is prime. February 10th, 2010, 05:28 PM   #8
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Re: An infinite number (?) of primes using the uple totient

Quote:
Originally Posted by CRGreathouse
Quote:
 Originally Posted by momo We begin by ?(1,x) We replace x by a number starting each time by 1 So we find 2 ---> ?(1,2) is equal to 5 (prime number) Then we continue ?(1,2,x) We find 3 ---> ?(1,2,3) = 13 (prime) and so on ....
Why 3? ?(1, 2, 2) = 11 is prime.
You are right.
When you work with Excel and you enter your data manually it happens.
Sorry for the mistake.
I have to recompute all the numbers!!!               February 10th, 2010, 05:35 PM #9 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Re: An infinite number (?) of primes using the uple totient Can you please send me the right sequence (minimal sequence because we can have a lot of sequences). Using Rapidshare will be very quick. Thank you! February 10th, 2010, 05:38 PM #10 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 I don't do Rapidshare, but here are the first 100: 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 This comes from the following Pari code: Code: phiset(v)=my(s=sum(i=1,#v,v[i]));sum(i=1,s,sum(j=1,#v,gcd(v[j],i)==1)) find(v)=v=vector(#v+1,i,if(i<=#v,v[i],1));for(i=1,9e9,v[#v]=i;if(isprime(phiset(v)),return(i))) v=;for(i=2,100,v=concat(v,find(v)));v You can run this to larger values if you like, just replace the "100" with something larger. Tags infinite, number, primes, totient, uple Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post caters Number Theory 67 March 19th, 2014 04:32 PM mathcool Number Theory 1 December 9th, 2011 04:58 AM momo Number Theory 5 February 23rd, 2010 10:02 AM Geir Number Theory 1 April 28th, 2009 05:00 AM mathcool Math Events 0 December 31st, 1969 04:00 PM

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