interlaced primes - Page 2

davar55 · 2013-12-30, 10:51

OK, very nice.

Too easy, you say? That's because of your great facility with primes.

The way I thought to make the problem more interesting is:

Call the the original interlace a 2-interlace.
find primes with a 2-interlace and a 3-interlace (the latter meaning
the three integers with indices == 0, 1, and 2 mod 3 are also prime).

If that's still "too easy" for 100, or 200, or 300 digit primes (or higher),
try raising the n-interlsce value, perhaps to n == #digits (if possible).

axn · 2013-12-30, 11:12

Quote:

Originally Posted by davar55

Call the the original interlace a 2-interlace.
find primes with a 2-interlace and a 3-interlace (the latter meaning
the three integers with indices == 0, 1, and 2 mod 3 are also prime).

If that's still "too easy" for 100, or 200, or 300 digit primes (or higher),
try raising the n-interlsce value, perhaps to n == #digits (if possible).

Actually, as n grows, the problem becomes easier! The number of full length candidates that need to be examined remains (statistically) the same. However, the size and count of the smaller primes drop, hence making the overall computation easier.

EDIT:- Hmmm... Perhaps I misread your proposal. You're looking for a prime that is simultaneously 2-interlaced _and_ 3-interlaced? That _would_ be tough.

davar55 · 2013-12-30, 11:20

Quote:

Originally Posted by axn

Actually, as n grows, the problem becomes easier! The number of full length candidates that need to be examined remains (statistically) the same. However, the size and count of the smaller primes drop, hence making the overall computation easier.

EDIT:- Hmmm... Perhaps I misread your proposal. You're looking for a prime that is simultaneously 2-interlaced _and_ 3-interlaced? That _would_ be tough.

Yes simultaneously. That may be tougher.

axn · 2013-12-30, 11:37

A small 40-digit solution:

Code:

6123287622616904596747948922513472803333

EDIT:- 80-digit solution:

Code:

96560692713215432725433099084511321271362597043193681463527122701557023009012193

EDIT2:- 100-digit "solution":

Code:

8408370377288719075150635331835934860753750749581487176353129019094739163381374267295631671772782779

This might be considered cheating, since one of the 3-interlaced primes starts with a leading zero.

davar55 · 2013-12-30, 16:44

Quote:

Originally Posted by axn

...

Code:

8408370377288719075150635331835934860753750749581487176353129019094739163381374267295631671772782779

This might be considered cheating, since one of the 3-interlaced primes starts with a leading zero.

Definitely NOT cheating by my OP. The lengths of
the interior primes was not constrained.

Jayder · 2013-12-30, 20:29

Could one of the largest known primes be interlaced in some way? If one of the larger mersenne primes were some large n interlaced that would be pretty cool. Hugely unlikely though. I will let somebody more skilled at code figure that out.

Batalov · 2013-12-30, 20:40

111*10^2997+220161228719621999 is a 3-interlaced prime.

It is also "partially" 2-interlaced:
10^1499+211279299 is prime and
11*10^1498+206281619 is not.

It is a 3-and-a-half-2-interlaced prime ;-)

Batalov · 2013-12-31, 02:17

111*10^597+815774285271319 is a 600-digit 3-and-2-interlaced prime.
Interlaced primes:
10^199+87223
10^199+17871
10^199+54519
10^299+85725739
11*10^298+1748211

Batalov · 2014-01-01, 11:59

111*10^1197+22554576678832733 is a 1200-digit 3-and-2-interlaced prime.

10^399+257733
10^399+246823
10^399+55687 are its 3-laces
10^599+254768373
11*10^598+25567823 are its 2-laces

henryzz · 2014-01-01, 12:37

Sounds a little crazy but could you add a 6-interlaced prime to the mix.

davar55 · 2014-10-09, 23:53

If one were to ask How Many 100- 200- or 300- digit numbers
were interlaced primes, would that be too hard to compute?
What n- digit value would be not too hard to count?

2013-12-30, 11:37	#15
axn Jun 2003 2²·3·421 Posts	A small 40-digit solution: Code: 6123287622616904596747948922513472803333 EDIT:- 80-digit solution: Code: 96560692713215432725433099084511321271362597043193681463527122701557023009012193 EDIT2:- 100-digit "solution": Code: 8408370377288719075150635331835934860753750749581487176353129019094739163381374267295631671772782779 This might be considered cheating, since one of the 3-interlaced primes starts with a leading zero. Last fiddled with by axn on 2013-12-30 at 12:24

2013-12-30, 20:29	#17
Jayder Dec 2012 2·139 Posts	Could one of the largest known primes be interlaced in some way? If one of the larger mersenne primes were some large n interlaced that would be pretty cool. Hugely unlikely though. I will let somebody more skilled at code figure that out. Last fiddled with by Jayder on 2013-12-30 at 20:31

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2013-12-30, 10:51	#12
davar55 May 2004 New York City 2·29·73 Posts	OK, very nice. Too easy, you say? That's because of your great facility with primes. The way I thought to make the problem more interesting is: Call the the original interlace a 2-interlace. find primes with a 2-interlace and a 3-interlace (the latter meaning the three integers with indices == 0, 1, and 2 mod 3 are also prime). If that's still "too easy" for 100, or 200, or 300 digit primes (or higher), try raising the n-interlsce value, perhaps to n == #digits (if possible).

2013-12-30, 20:40	#18
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9477₁₀ Posts	11110^2997+220161228719621999 is a 3-interlaced prime. It is also "partially" 2-interlaced: 10^1499+211279299 is prime and 1110^1498+206281619 is not. It is a 3-and-a-half-2-interlaced prime ;-)

2013-12-31, 02:17	#19
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22405₈ Posts	11110^597+815774285271319 is a 600-digit 3-and-2-interlaced prime. Interlaced primes: 10^199+87223 10^199+17871 10^199+54519 10^299+85725739 1110^298+1748211

2014-01-01, 11:59	#20
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶·13 Posts	11110^1197+22554576678832733 is a 1200-digit 3-and-2-interlaced prime. 10^399+257733 10^399+246823 10^399+55687 are its 3-laces 10^599+254768373 1110^598+25567823 are its 2-laces

2014-01-01, 12:37	#21
henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 2³·3·5·7² Posts	Sounds a little crazy but could you add a 6-interlaced prime to the mix.

2014-10-09, 23:53	#22
davar55 May 2004 New York City 2×29×73 Posts	If one were to ask How Many 100- 200- or 300- digit numbers were interlaced primes, would that be too hard to compute? What n- digit value would be not too hard to count?