Predict M52

[Uncwilly]

Please keep posts specific to the topic of the thread.

[Dr Sardonicus]

If two or more predictions for M52 are verified, and if there is any question of which prediction was made first, the potential time stamp issue might become a real issue.

Until then,...

[chalsall]

Originally Posted by Uncwilly

Please keep posts specific to the topic of the thread.

Many believe that trying to manage the MF is a bit like Herding Cats.

At the same time, Humor is such a subjective thing.

Sorry for "taking the piss". But, come on... It's fun playing with really smart people (along with a few 'bots)...

[retina]

Originally Posted by Dr Sardonicus

... the potential time stamp issue might become a real issue.

What issue?

This whole thread is just for bragging rights. The best guesser (i.e. the "winner") isn't going to be sent money, the nuclear launch codes⁰, or indeed anything at all.

⁰ Psst, the launch code is '00000000'. Don't tell anyone.

[Dr Sardonicus]

Originally Posted by retina

What issue?

This whole thread is just for bragging rights.
<snip>

There is a sentiment (variously formulated) known as Sayre's Law, q.v.

[Paimon2005]

The 52nd Mersenne Prime maybe among 2^57885161-1(I don't know whether any other prime exists except 2^57885161-1, 2^74207281-1, 2^77232917 and 2^82589933-1) or not) to 2^158729803-1(158729803 is the largest prime which smaller than 158729866)
I calculated exponent of each prime divides that of previous one, and I cut the 5 biggest quotients and 5 smallest ones, got remained 40 quotients. I continued to calculate the average(avg, 1.3936846) and standard deviation(stdev, 0.3073011) of remained 40 quotients. From them I got 82589933*(avg-3*stdev)=38964385.1, 82589933*(avg+3*stdev)=158729866.1

See the pdf given.

[Paimon2005]

Originally Posted by Paimon2005

The 52nd Mersenne Prime maybe among 2^57885161-1(I don't know whether any other prime exists except 2^57885161-1, 2^74207281-1, 2^77232917 and 2^82589933-1) or not) to 2^158729803-1(158729803 is the largest prime which smaller than 158729866)
I calculated exponent of each prime divides that of previous one, and I cut the 5 biggest quotients and 5 smallest ones, got remained 40 quotients. I continued to calculate the average(avg, 1.3936846) and standard deviation(stdev, 0.3073011) of remained 40 quotients. From them I got 82589933*(avg-3*stdev)=38964385.1, 82589933*(avg+3*stdev)=158729866.1

See the pdf given.

Well, 3-Sigma Guidelines told us that values are almost all(99.73%) between μ-3σ to μ+3σ

[kriesel]

By definition, because of magnitude sorting, Mp#52 > Mp#51* (M(82589933) assuming no more are found below p=82589933, which is very likely the case). Its probability distribution is therefore highly asymmetric; there is zero probability of Mp#52 < Mp#51. (See skewness https://en.wikipedia.org/wiki/Skewness)

The normal distribution is symmetric. https://en.wikipedia.org/wiki/Normal_distribution
It is also unbounded. And continuous.
The normal distribution does not apply to Mersenne primes' exponents or ln(Mp exponent).
It's thought the Poisson distribution does. https://en.wikipedia.org/wiki/Poisson_distribution

Plus or minus four standard deviations contains ~0.9999366 of the normal distribution's population. But -4 times the standard deviation you computed ~ 4 * -.3073 ~ -1.2292, admitting a 0.00317% chance of <-1.2292, or for Mp#52, p < -18,929,612. That's a long ways from > 82589933.
Mersenne numbers by definition are integers that might be primes, and so only occur for integer exponent p > +1.

Further, GIMPS verification is complete up to almost M(61475119) currently. That's within 1 SD of M(82589933).
Below -1 SD of mean is ~ 0.158655 chance of Mp#52 < Mp#51, a contradiction. And there's near zero chance of a missed Mersenne prime below there (at p < 61475119).

Computation of standard deviation may make sense for data that are normally distributed or close to it.
This is not.

[billymac00]

110687989

May 11 2023

[Raydex]

As a reminder, there were 1331 days between the discovery of M_42643809 and M_57885161.

https://www.timeanddate.com/date/dur...&d2=25&y2=2013

We are now at 1372 days since December 7, 2018, so we have long surpassed that record.

Anyway, for my prediction:

115,200,023

December 25, 2022

[Uncwilly]

Originally Posted by Raydex

Anyway, for my prediction:

115,200,023

December 25, 2022

That date was already guessed.

Originally Posted by MattcAnderson

I want to add another guess. My second exponent is 90000049. (a prime number) It's corresponding date is December 25, 2022.

Therefore rule 3 applies:

Originally Posted by Uncwilly

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.
...
6 You may post 3 guesses (for each number and date). If all exponents 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.

You can guess the number again in 60 days.