Prime numbers and primality testing Yahoo Group Russell E. Rierson's Question About Prime Numbers =============================================== Zak Seidov Message 2 of 6 Sep 29, 2003 ----------------------------------------------- This is copy of my post (sorry for those reading this twice): For p=11, minimal d = 4911773580 (OEIS A088430), and AP contains maximal number, 11, primes. For p=13, d should be a factor of 2310. Who first find it (and then try 17,19,...)? Zak BTW I guess that found d is indeed minimal not unique- there is no reason of absense of other larger d's. On 28 Sep 2003, Russell E. Rierson wrote (http://www.mathforum.org/discuss/sci.math/m/133406/540774): >Twin primes are prime numbers such as 5 and 7, 11 and 13, 17 and 19, >etc. These twins are only one unit apart. > >There are strings of prime numbers that are n-units apart: > >3, 5, 7, [3 prime numbers, 2 units apart] > >5, 11, 17, 23, 29, [5, 6 units] > >7, 157, 307, 457, 607, 757, 907, [7, 150 units] > >11... ? ...? ...? ... > >The question becomes: For all odd prime numbers P, are there P number of >primes that are the same numerical[equal] distance apart? =============================================== mad37wriggle Message 3 of 6 Sep 30, 2003 ----------------------------------------------- By my calculation the smallest d for p=11 is 1536160080. Have I made a mistake? Richard --- In primenumbers@yahoogroups.com, "Zak Seidov" wrote: > This is copy of my post > (sorry for those reading this twice): > > For p=11, > minimal d = 4911773580 (OEIS A088430), > and AP contains maximal number, 11, primes. > > For p=13, d should be a factor of 2310. > Who first find it (and then try 17,19,...)? > Zak > > > BTW I guess that found d is indeed minimal not unique- > there is no reason of absense of other larger d's. > > > On 28 Sep 2003, Russell E. Rierson wrote > (http://www.mathforum.org/discuss/sci.math/m/133406/540774): > >Twin primes are prime numbers such as 5 and 7, 11 and 13, 17 and 19, > >etc. These twins are only one unit apart. > > > >There are strings of prime numbers that are n-units apart: > > > >3, 5, 7, [3 prime numbers, 2 units apart] > > > >5, 11, 17, 23, 29, [5, 6 units] > > > >7, 157, 307, 457, 607, 757, 907, [7, 150 units] > > > >11... ? ...? ...? ... > > > >The question becomes: For all odd prime numbers P, are there P > number of > >primes that are the same numerical[equal] distance apart? =============================================== Ken Davis Message 4 of 6 Sep 30, 2003 ----------------------------------------------- This is posted on behalf of richyfortythree cheers Ken > By my calculation the smallest d for p=11 is > 1536160080. Have I > made a > mistake? 1536160080 is also what I get. (Same mistake maybe?) Cheers richyfourtythree --- In primenumbers@yahoogroups.com, "mad37wriggle" wrote: > > By my calculation the smallest d for p=11 is 1536160080. Have I made a > mistake? > > Richard > > > --- In primenumbers@yahoogroups.com, "Zak Seidov" > wrote: > > This is copy of my post > > (sorry for those reading this twice): > > > > For p=11, > > minimal d = 4911773580 (OEIS A088430), > > and AP contains maximal number, 11, primes. > > > > For p=13, d should be a factor of 2310. > > Who first find it (and then try 17,19,...)? > > Zak > > > > > > BTW I guess that found d is indeed minimal not unique- > > there is no reason of absense of other larger d's. > > > > > > On 28 Sep 2003, Russell E. Rierson wrote > > (http://www.mathforum.org/discuss/sci.math/m/133406/540774): > > >Twin primes are prime numbers such as 5 and 7, 11 and 13, 17 and 19, > > >etc. These twins are only one unit apart. > > > > > >There are strings of prime numbers that are n-units apart: > > > > > >3, 5, 7, [3 prime numbers, 2 units apart] > > > > > >5, 11, 17, 23, 29, [5, 6 units] > > > > > >7, 157, 307, 457, 607, 757, 907, [7, 150 units] > > > > > >11... ? ...? ...? ... > > > > > >The question becomes: For all odd prime numbers P, are there P > > number of > > >primes that are the same numerical[equal] distance apart? =============================================== Zak Seidov Message 5 of 6 Sep 30, 2003 ----------------------------------------------- Yes, Richard and Ken, there is mistake - on my side, my "d" is larger than yours... Zak --- In primenumbers@yahoogroups.com, "Ken Davis" wrote: > This is posted on behalf of > richyfortythree > cheers > Ken > > By my calculation the smallest d for p=11 is > > 1536160080. Have I > > made a > > mistake? > > 1536160080 is also what I get. (Same mistake maybe?) > > Cheers > > richyfourtythree > > > --- In primenumbers@yahoogroups.com, "mad37wriggle" > wrote: > > > > By my calculation the smallest d for p=11 is 1536160080. Have I > made a > > mistake? > > > > Richard > > > > > > --- In primenumbers@yahoogroups.com, "Zak Seidov" > > wrote: > > > This is copy of my post > > > (sorry for those reading this twice): > > > > > > For p=11, > > > minimal d = 4911773580 (OEIS A088430), > > > and AP contains maximal number, 11, primes. > > > > > > For p=13, d should be a factor of 2310. > > > Who first find it (and then try 17,19,...)? > > > Zak > > > > > > > > > BTW I guess that found d is indeed minimal not unique- > > > there is no reason of absense of other larger d's. > > > > > > > > > On 28 Sep 2003, Russell E. Rierson wrote > > > (http://www.mathforum.org/discuss/sci.math/m/133406/540774): > > > >Twin primes are prime numbers such as 5 and 7, 11 and 13, 17 and > 19, > > > >etc. These twins are only one unit apart. > > > > > > > >There are strings of prime numbers that are n-units apart: > > > > > > > >3, 5, 7, [3 prime numbers, 2 units apart] > > > > > > > >5, 11, 17, 23, 29, [5, 6 units] > > > > > > > >7, 157, 307, 457, 607, 757, 907, [7, 150 units] > > > > > > > >11... ? ...? ...? ... > > > > > > > >The question becomes: For all odd prime numbers P, are there P > > > number of > > > >primes that are the same numerical[equal] distance apart? =============================================== Zak Seidov Message 6 of 6 Oct 1, 2003 ----------------------------------------------- Russell sent me Phil's message with p=13 and p=17! Here is this message with my editings (sorry Phil!) %%%%%%% NMBRTHRY archives -- November 2001 (#9) Date: Wed, 7 Nov 2001 09:17:30 -0500 Reply-To: Phil Carmody Sender: Number Theory List From: Phil Carmody Subject: Prime-producing Linear Polynomials The linear polynomial f(X) = dX+q can have at most q successive terms f(0)...f(q-1) prime, (and q must be prime for f(0) to be prime, evidently). It remains an open question, and one with few data-points, whether such maximal q-based q-length Arithmetic Progressions exist for every q. q=3, d=2 yield the primes 3,5,7; q=5, d=6 yield the primes 5,11,17,23,29; q=7, d=150 yield the primes 7,157,307,457,607,757,907. In 1986, Löh discovered for q=11 d=1536160080, and for q=13 d=9918821194590. [The above was a synthesis of what Paulo Ribenboim has in The New Book of Prime Number Records] At the start of 2001 I started tackling the q=17 problem, and I wrote some brute force code to attack it. The code was peppered with bugs, and despite finding a record Cunningham Chain with the broken code http://listserv.nodak.edu/scripts/wa.exe?A2=ind0103&L=nmbrthry&P=R423 I gave up both on the project and the code. However, I recently encountered other tasks which seemed like a good target for the code, and easier than the Arithmetic Progression problem, and resolved to de-mothball the code. Within a day of thinking this, Tom Hadley posted the very result I thought I might search for - a minimal 15-tuple ( http://www.ltkz.demon.co.uk/kt15.txt ). Rather than kill the idea, this encouraged me! So I (think I) fixed the bugs, and started the search again. After roughly 5 days on a single 533MHz Alpha (21164), I found the following result, finally toppling the 15-year-old record. The record is now q=17 d=341976204789992332560 And the primes are q=19 anyone? (The scaling factors indicate that it might be possible with a collaborative effort, and my code parallelises) Thanks go to Tom Hadley for giving me a massive kick up the arse last week and to Paul Jobling who has been a useful resource on how to apply intelligence to brute force problems since the project began. Phil %%%%%%%%%%%%5 --- In primenumbers@yahoogroups.com, "Zak Seidov" wrote: > Yes, Richard and Ken, > there is mistake - > on my side, > my "d" is larger than yours... > Zak > > --- In primenumbers@yahoogroups.com, "Ken Davis" wrote: > > This is posted on behalf of > > richyfortythree > > cheers > > Ken > > > By my calculation the smallest d for p=11 is > > > 1536160080. Have I > > > made a > > > mistake? > > > > 1536160080 is also what I get. (Same mistake maybe?) > > > > Cheers > > > > richyfourtythree > > > > > > --- In primenumbers@yahoogroups.com, "mad37wriggle" > > wrote: > > > > > > By my calculation the smallest d for p=11 is 1536160080. Have I > > made a > > > mistake? > > > > > > Richard > > > > > > > > > --- In primenumbers@yahoogroups.com, "Zak Seidov" > > > wrote: > > > > This is copy of my post > > > > (sorry for those reading this twice): > > > > > > > > For p=11, > > > > minimal d = 4911773580 (OEIS A088430), > > > > and AP contains maximal number, 11, primes. > > > > > > > > For p=13, d should be a factor of 2310. > > > > Who first find it (and then try 17,19,...)? > > > > Zak > > > > > > > > > > > > BTW I guess that found d is indeed minimal not unique- > > > > there is no reason of absense of other larger d's. > > > > > > > > > > > > On 28 Sep 2003, Russell E. Rierson wrote > > > > (http://www.mathforum.org/discuss/sci.math/m/133406/540774): > > > > >Twin primes are prime numbers such as 5 and 7, 11 and 13, 17 > and > > 19, > > > > >etc. These twins are only one unit apart. > > > > > > > > > >There are strings of prime numbers that are n-units apart: > > > > > > > > > >3, 5, 7, [3 prime numbers, 2 units apart] > > > > > > > > > >5, 11, 17, 23, 29, [5, 6 units] > > > > > > > > > >7, 157, 307, 457, 607, 757, 907, [7, 150 units] > > > > > > > > > >11... ? ...? ...? ... > > > > > > > > > >The question becomes: For all odd prime numbers P, are there P > > > > number of > > > > >primes that are the same numerical[equal] distance apart? =============================================== Cached by Georg Fischer at Nov 14 2019 12:46 with clean_yahoo.pl V1.4