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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

1498.0. "Primes in Arith. Progression" by CIVAGE::LYNN (Lynn Yarbrough @WNP DTN 427-5663) Fri Oct 04 1991 18:22

Here's an idea about primes in Arithmetic Progression that I haven't seen 
yet, although I have seen similar topics in this conference:

Consider the sequences:
{2,3}
	2 primes in A.P., delta = 1
{3,5,7} 
	3 primes in A.P., delta = 2
{5,11,17,23,29} 
	5 primes in A.P., delta = 6 = 2*3
{7,157,307,457,607,757,907} 
	7 primes in A.P., delta = 150 = 2*3*5*5

Thus for each of the primes p considered, we have a progression of primes of 
length p, starting with p.

Delta must be a multiple of the previous primes: otherwise, any progression
of length equal to an omitted prime must contain a multiple of it and thus
be composite. 

Does this grand sequence continue indefinitely? So far I haven't find a 
progression for p = 11, having tried Delta from 1*2*3*5*7 to 1000*2*3*5*7.

T.R	Title	User	Personal Name	Date	Lines
1498.1		ZFC::deramo	insufferably cute	`Fri Oct 04 1991 21:25`	3
	See also topic 4, Primes in A.P. Dan
1498.2	(Yawn)	CIVAGE::LYNN	Lynn Yarbrough @WNP DTN 427-5663	`Fri Nov 15 1991 11:08`	5
	>Does this grand sequence continue indefinitely? So far I haven't find a >progression for p = 11, having tried Delta from 12357 to 10002357. It looks discouraging. I have run the test out to delta = 1500002357 without success.
1498.3		ZFC::deramo	All the leaves are brown and the sky is gray.	`Fri Nov 15 1991 11:51`	5
	To ask for a prime progression of a given length is one thing, but methinks to expect it to also start at p = 11 is far too optimistic. Dan
1498.4	Lynn's Lemma is in jeopardy	VMSDEV::HALLYB	Fish have no concept of fire	`Fri Nov 15 1991 13:10`	11
	> To ask for a prime progression of a given length is one thing, > but methinks to expect it to also start at p = 11 is far too > optimistic. Such is the nature of discovery. 'Twould be nice if the hypothesis generalizes. Maybe Lynn should get on the net and offer a $100 prize for (the first) example sequence. There are lots of bored students with idle CPUs... John
1498.5	I'll use my own CPU, thanks :-)	CIVAGE::LYNN	Lynn Yarbrough @WNP DTN 427-5663	`Fri Nov 15 1991 13:18`	4
	> Maybe Lynn should get on the net and offer a $100 prize for (the first) > example sequence. There are lots of bored students with idle CPUs... Maybe John should put up the money!
1498.6	any near misses?	ZFC::deramo	Dan D'Eramo	`Fri Nov 15 1991 13:43`	4
	What is the longest prime arithmetic progression found so far starting with p=11? Dan
1498.7	Who looks at short ones :-)?	CIVAGE::LYNN	Lynn Yarbrough @WNP DTN 427-5663	`Mon Nov 18 1991 10:34`	14
	>What is the longest prime arithmetic progression found so far starting with >p=11? The longest I have observed is seven primes with delta = 123480: 11 123491 246971 370451 493931 617411 740891 followed by 907953, then 987891 for 8 out of 9. Since I don't normally display them, I may have bypassed many longer sequences. By the way, long sequences of composites* of this form are not all that common: 14 is the longest of those I have seen. I ran the program out to delta = 1,000,0002357 over the weekend, without success. Maybe I should pick an easier problem :-)
1498.8	Interest at the $25 level, not the $100 level.	VMSDEV::HALLYB	Fish have no concept of fire	`Tue Nov 19 1991 16:58`	16
	> Since I don't normally display them, I may have bypassed many longer > sequences. Though it makes sense, it escaped me that you want an A.P. of -exactly- the specified length. > Maybe John should put up the money! If you can get others to front you $75, I'll put up $25. Some of you may know the name of E. Karst in reference to this topic. He was a friend and user of idle time on an IBM 1130 back in the late 60s and early 70s, hunting for primes in A.P. Thus I have some personal interest in furthering research in this field. John