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2022-11-26, 01:56   #67
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

32·1,117 Posts

Quote:
 Originally Posted by kruoli As long as we have the 1 at the end, why shouldn't there be other prime possible?
Good point, I have not checked. The idea to use those k*10^n+1 was a momentary lapse of reason,
I just looked at a few similar ones from UTM top (even with one-digit k values, they have "1", "k" and "0"s and there are enough permutations to kill them). Those are not good - I concur.

My best find (a day or two ago), then, is still the best -
(4*10^348453+41)/9 <348453 digits> 444444...444449
followed by some similar ones:
(5*10^343734+31)/9 <343734 digits> 55555...555559
(5*10^335480+31)/9 <335480 digits> 55555...555559
etc

There could be a good one hiding in this list, but someone needs to run all permutations:
Code:
rank	prime               	digits	who	when	comment
224	10^1888529-10^944264-1	1888529	p423	Oct 2021	Near-repdigit
269	993 · 10^1768283 - 1	1768286	L4879	Feb 2019	Near-repdigit
270	9 · 10^1762063 - 1	1762064	L4879	Aug 2020	Near-repdigit
283	8 · 10^1715905 - 1	1715906	L4879	Aug 2020	Near-repdigit
318	9992 · 10^1567410 - 1	1567414	L4879	Aug 2020	Near-repdigit
328	99 · 10^1536527 - 1	1536529	L4879	Feb 2019	Near-repdigit
330	992 · 10^1533933 - 1	1533936	L4879	Feb 2019	Near-repdigit

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