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Message boards : Seventeen or Bust : Prime Guessing Game

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Kevonni

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Message 119084 - Posted: 28 Jun 2018 | 8:49:28 UTC

Let's start guessing what the next prime will be like with the Fermat prime pool.

JeppeSN

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Message 119089 - Posted: 28 Jun 2018 | 12:16:03 UTC - in response to Message 119084.

In the Fermat prime pool, people express their bids as b values (the b in b^(2^n)+1).

Here we want to guess for the next prime that eliminates any of the five remaining multipliers in the SierpiÅ„ski problem, I presume.

Should we state our guess as the value of the exponent n in the expression

kÂ·2^n + 1,

or should we give the number of decimal digits?

/JeppeSN

Michael Goetz
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Message 119090 - Posted: 28 Jun 2018 | 12:35:09 UTC

Date is another possibility, e.g., "We'll find the next prime in 2023."

Also, bear in mind that we're currently in the middle of a long double check of prior work, with much lower chances of finding a prime. While the numbers themselves are smaller (which increases chances), since the numbers have already been checked once, our chance of finding a prime is approximately 30 times lower than it normally would be.

Even without the double check, there were nine years between the discoveries of the last 2 primes. The gap between the 2 largest primes is pretty large: n=13M and n=31M.

____________
My lucky number is 75898524288+1

Keith
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Message 119092 - Posted: 28 Jun 2018 | 12:54:11 UTC

The next K to be eliminated could be another possibility, or the date AND the next K.
____________
My Primes
Badge Score: 2*1 + 3*1 + 4*2 + 6*4 + 7*9 + 9*1 + 10*2 = 129

Chara34122

Joined: 11 Feb 17
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Message 119093 - Posted: 28 Jun 2018 | 13:05:59 UTC

I thought about it while I was participating in original SoB and my opinion was:
1. Next k would be 24737 or 55459 (but not 10223 because I did not know that it was PrimeGrid's part of search)
2. I expected it in the short period of time (n<2^25)

Now my expectation is:
1. One of these 2 k's also
2. n<2^26 (Maybe in 2024?)

JeppeSN

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Message 119095 - Posted: 28 Jun 2018 | 13:17:49 UTC

It may be a matter of taste, but I find it uninteresting to bet on which k will be eliminated next (I was about to write "that is pure lottery", but gambling on the size of the next SoB prime is a lottery as well, I guess).

My guess for the exponent (of 2) of the next SoB prime shall be:

n = 17.8 M

that is k Â· 2^{17,800,000} + 1 for some k in { 21181; 22699; 24737; 55459; 67607 }.

I know I will win, and then Michael Goetz can predict when the leading edge will be near n = 17.8 M.

/JeppeSN

JeppeSN

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Message 119097 - Posted: 28 Jun 2018 | 13:21:54 UTC - in response to Message 119093.

2. n<2^2^26 (Maybe in 2024?)

You mean the prime will be (just) below 2^(2^26), then what we usually call n (the n in kÂ·2^n + 1) will be close to 2^26 = 67 million?

/JeppeSN

Chara34122

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Message 119098 - Posted: 28 Jun 2018 | 13:29:20 UTC - in response to Message 119097.

n Just below 67000000. So I think. And 17.8 million range already passed or I mistake something?

I've corrected it.

JeppeSN

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Message 119101 - Posted: 28 Jun 2018 | 14:39:59 UTC - in response to Message 119098.

n Just below 67000000. So I think. And 17.8 million range already passed or I mistake something?

You are right! My guess was meaningless :-(

The double-check is currently near n = 25 M according to stats_sob_llr, and the double check will end near n = 31.6 M.

I will come up with a meaningful guess at another time (I guess I committed hubris with the style in my post where I made the silly guess).

/JeppeSN

Michael Goetz
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Message 119102 - Posted: 28 Jun 2018 | 15:09:20 UTC - in response to Message 119101.

...the double check will end near n = 31.6 M.

Nothing above 31M needs to be double checked. The 31M range was always PrimeGrid's, so the part that's done is fully double checked already.

The double check ends at n=30,999,908.
____________
My lucky number is 75898524288+1

Kevonni

Joined: 20 Jun 13
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Message 119110 - Posted: 29 Jun 2018 | 1:23:21 UTC - in response to Message 119089.

The guess should be stated as the exponent that will eliminate the next k. I am personally betting on the range from 3700097 to 37911100.

JeppeSN

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Message 119114 - Posted: 29 Jun 2018 | 6:47:53 UTC

OK, I will bring a valid bid, then: n = 48,400,000.

/JeppeSN

Message boards : Seventeen or Bust : Prime Guessing Game