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Old 2021-12-08, 20:48   #1
Batalov
 
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Mar 2008
Phi(4,2^7658614+1)/2

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Question Predict n for the third (future) (PR)prime Smr(n)

Quote:
Originally Posted by NJAS
If you write the numbers in descending order, 1, 21, 321, 4321, 54321, ..., "n n-1 ... 321" (this is A000422 in the OEIS), then two (PR)primes are known, for n = 82 and 37765 . This is A176024, but it only has 2 terms. Can you get one more term? This might be child's play for you!
With 2 terms previously found and verified and some people searching for the next one , let's guess 3rd term of A176024 (specifically, the next, currently unknown, yet to be noticed by a human.)

THE RULES OF THE GAME:
  1. Post your guess here, no PM'ing.
  2. Your guess must include a number (we are guessing the function argument) and/or date of discovery. No ranges, they may be ignored (or we may take the worst case of the range as the choice.) Failure to guess an eligible number will count against you and impose a wait as in rule 6.
  3. You can not guess a number (or date) that has already been guessed. If you do guess a number or date that has already been submitted, this will count against you and impose a wait as in rule 6.
  4. If you guess a number that has known factor, at the time you posted, your guess will be ignored. Guessing a number with a known factor will count against you and impose a wait as in rule 6.
  5. If there is a tie (i.e. 2 posts are equally close and meet all other rules), the first post gets it.
  6. You may post 2 guesses (for each number and date). If all n's up to your number have had a first time test (or DC), you may select another, after a 60 day wait. Same (60 day wait) for date predictions that have passed.
  7. All guesses received within the 48 hours before A176024(3) is reported (by or to anyone by any method) are hereby disqualified (to prevent cheating). This disqualification period will extend through to the time that a person reports to the forum that a candidate prime has been noticed. When that happens all guessing is closed.
  8. For the sake of this game, we will use the date (in UTC) that the prime is reported to and recorded. This may differ from the officially reported discovery date.
Absurd guesses may be ignore it any statistical reports or graphs.
Rules may be clarified later. New rules for the next game may be suggested in this thread.
Make your guess clear in your post.

GAME ON!
___________
*Eligible in this case is different from the other guessing game. Y'all know that there n must be prime.
Here, at the very least, numbers for which Smr(n) is divisble by 3, 7, or 11 will be considered "absurd". The obvious rule of divisibility by 3 is easily found. Or else, please make sure that you at least run
pfgw -f -q"Smr(my_favorite_n)"
and it doesn't immediately produce a factor.
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Old 2021-12-08, 20:54   #2
Batalov
 
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Phi(4,2^7658614+1)/2

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I will bet on 777,727 and 12/25/2021. I am an optimist.
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Old 2021-12-09, 01:24   #3
ryanp
 
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Boulder, CO

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Am I allowed to guess?
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Old 2021-12-09, 05:13   #4
Batalov
 
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Phi(4,2^7658614+1)/2

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Sure thing. Hint: guessing too close to another guess shares territory between guesses in half.

It's best to sparse them out. Guesses are like ...holes - everyone's got one.

Guesses are just like playing preference or sports bridge - you just need to play it best given the prior data (your and your partner's 26 cards).
If you are worse than statistical expectation even if you take 12 hands but you were expected to take 13, in a bridge tournament you will get a demerit.
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