## Prime gap of 337446, merit 18.33

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• Torbjörn Alm and I have found a prime gap of 337446 between 7996-digit prp s. PrimeForm/GW prp ed. The initiating prp 1009461925.....1170696317 has no simple
Message 1 of 5 , Nov 25 4:20 PM
Torbjörn Alm and I have found a prime gap of 337446 between 7996-digit prp's.
PrimeForm/GW prp'ed.
The initiating prp 1009461925.....1170696317 has no simple expression.
The decimal expansion is at The Top-20 Prime Gaps:
http://hjem.get2net.dk/jka/math/primegaps/gaps20.htm

The average gap near p is around log p. gap/log p is called the merit.
This gap has merit 18.33 and is the largest known gap with merit above 14.70.
Rough heuristics say 1 of e^18.33 = 91 million random gaps have merit above
18.33. The gap was not random.

Jose Luis Gomez Pardo found the largest known gap with proven endpoints.
That gap is 233822 betweeen 5878-digit primes proved by him with Marcel
Martin's Primo. The merit is 17.28.

Our gap could be a future candidate for largest proven gap. 7996 digits
(twice) is above the Primo record and a bit much today, so no proofs are
currently planned.

--
Jens Kruse Andersen
• ... François Morain has now proved those prp s with fastECPP. This makes it the largest known gap between proven primes. More details at
Message 2 of 5 , May 1, 2005
In http://groups.yahoo.com/group/primeform/message/5059 I wrote:

> Torbjörn Alm and I have found a prime gap of 337446 between 7996-digit prp's.
> PrimeForm/GW prp'ed.

François Morain has now proved those prp's with fastECPP.
This makes it the largest known gap between proven primes.

More details at http://hjem.get2net.dk/jka/math/primegaps/gap337446.htm

--
Jens Kruse Andersen
• I encouraged Jens to ask Francois to do ECPP on this worthy target and am delighted to see the endpoints proven. Now Jens has to work out how to enter the two
Message 3 of 5 , May 1, 2005
I encouraged Jens to ask Francois to do ECPP
on this worthy target and am delighted to see
the endpoints proven.

Now Jens has to work out how to enter the two
ECPP-listable "blobs", as I did for an endpoint in

http://primes.utm.edu/primes/page.php?id=28903

(proof of the other endpoint was abandoned when the gap
hunters got smarter:-)

David
• ... Thanks. The Prime Pages does not record prime gaps so the end points only qualify because ECPP was used. Arbitrary prp s of this size are easy to find so
Message 4 of 5 , May 1, 2005

> I encouraged Jens to ask Francois to do ECPP
> on this worthy target and am delighted to see
> the endpoints proven.
>
> Now Jens has to work out how to enter the two
> ECPP-listable "blobs"

Thanks.
The Prime Pages does not record prime gaps so the end points only qualify
because ECPP was used.
Arbitrary prp's of this size are easy to find so François and I agreed to credit
the primes to the existing:
FE1 Morain, FastECPP

Morain's password must be used for this prover code but he has not reacted to my
submission instructions.
I have entered the decimal expansions as prime_blob_134 and prime_blob_135
without prover code and password, but that is required at the final submission.
Maybe Chris would step in?
In case of concern that this is a fraud (like the last FastECPP submissions), my
http://hjem.get2net.dk/jka/math/primegaps/gap337446.htm

--
Jens Kruse Andersen
• ... Chris will agree to record endpoints via a tolerated coment , if they qualified on other grounds, as here: 16282536218213511214...(5838 other
Message 5 of 5 , May 1, 2005
Jens:

> The Prime Pages does not record prime gaps

Chris will agree to record endpoints
via a "tolerated coment",
if they qualified on other grounds, as here:

"16282536218213511214...(5838 other digits)...95781943818436478311"
5878 c28 2003 ECPP, Stop gap

"16282536218213511214...(5838 other digits)...95781943818436244489"
5878 c28 2003 Start gap, ECPP

39877"Gaps20_PrP3397a-110070"
3397 c19 2002 Start gap, ECPP
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