## 22578Re: [PrimeNumbers] Relatively major problem ripe for expansion

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• Feb 7, 2011
James Merickel wrote:
> On another note, I haven't heard back from Jens on an offer of sharing
> credit for a nice titanic curio I put in his hands for proof, leading me to
> believe he's working on it. I don't suppose there's likely to be any harm
> done by stating it now, since he would have had quite a number of hours with
> it. The first titanic near-repunit prime with a near-repunit prime number
> of digits, (10^1117-1)/9+4*10^92, is the 101st such prime (of any size),
> assuming no rare ispseudoprime false positive and defining near-repunits to
> necessarily have at least 3 digits.

You mailed me less than a day ago. Following up on your work is not all I do,
and I don't want to share a curio just because I verified it afterwards.
However, after seeing your post here I have confirmed it is the 101st prp.
Marcel Martin's Primo has proved the first 77 prp's and the last.
I skipped the remaining 23 which have 811 and 911 digits:
(10^811-1)/9+6*10^14
(10^811-1)/9+6*10^82
(10^811-1)/9+4*10^115
(10^811-1)/9+6*10^155
(10^811-1)/9+7*10^216
(10^811-1)/9+7*10^242
(10^811-1)/9+7*10^388
(10^811-1)/9+7*10^406
(10^811-1)/9+4*10^480
(10^811-1)/9+6*10^530
(10^811-1)/9+4*10^577
(10^811-1)/9+1*10^600
(10^911-1)/9+8*10^327
(10^911-1)/9+6*10^357
(10^911-1)/9+6*10^402
(10^911-1)/9+5*10^465
(10^911-1)/9+2*10^475
(10^911-1)/9+6*10^707
(10^911-1)/9+5*10^717
(10^911-1)/9+8*10^732
(10^911-1)/9+6*10^792
(10^911-1)/9+6*10^795
(10^911-1)/9+2*10^890

It might take around half a GHz day to verify them with Primo from
http://www.ellipsa.eu/public/primo/primo.html

The 23 input files can quickly be made with
http://users.cybercity.dk/~dsl522332/math/certif/primoin.zip

--
Jens Kruse Andersen
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