Predict "M51"

[LaurV]

Originally Posted by lavalamp

Note that these are all larger exponents though. My argument still stands.

No it does not. He only linked his domain of interest, but you can always decrease the lower boundary of that link.

[lavalamp]

Originally Posted by LaurV

No it does not. He only linked his domain of interest, but you can always decrease the lower boundary of that link.

Slightly moot now as it was factored with P-1 2 months ago, a 93 bit factor.

I'll change my guess to 92304749, same date.

[kriesel]

Originally Posted by LaurV

No it does not. He only linked his domain of interest, but you can always decrease the lower boundary of that link.

Or, looking very broadly at exponents, there are many further trial factored than the claim. https://www.mersenne.org/report_fact...=1&tftobits=72 Some few of those upper exponents TF to >80 bits are my output. I wasn't aware of that search capability til now; nice.

[kriesel]

Ok, just for fun:

    Ballpark    Basis of ballpark                        Guess exp        Date guess                
51a    80,381,917    ratio of previous two, go up to the next unassigned/expired    80382067         Jun 14, 2018    Flag Day in the US            
51b    113,977,250    Approx expected ratio 1.47576*p50?                113977277         Aug 26, 2022    Assuming 8 million/year first test range progress        
51c    376,059,344    A long stride, 521/107*p50?                         376059389         Nov 30, 2052    "

The 8 million per year assumption is based on exponents getting harder as we go up, canceled out by computers getting faster with time, and the number of participants and systems per participant not changing much, but no major breakthroughs in number theory or revelations by ET. (Confirming or disproving a list of a select set of candidates would be way faster than exhaustive search of a great many candidates in a range.)

Ugh, getting to 376M with the wave of lowest available first time checks may take a depressingly long time, well past my likely expiration date, under the preceding assumptions, plus even good luck in the actuarial tables.

[kriesel]

Originally Posted by Prime95

So we would expect the exponent of GIMPS' sixteenth prime to be around 636 million...

    1257787 (last Slowinski prime)
    1856192
    2739294
    4042540
    5965819
    8804116
    12992763
    19174200
    28296517
    41758868
    61626067
    90945284
    134213412
    198066786
    292299040
    431363231
    636588601

...or maybe we're just awfully lucky!

Indeed, we are lucky. For the first time in history, the mean ratio between known Mersenne prime exponents is both below 1.47576... and trending downward. We expect to find on the average, ~5.92 per decade of exponent, and that series is (digits,number)=
1,4
2,6
3,4
4,8
5,6
6,5
7,5
8,12? 10^7 - 10^8, expected ~47 through 10^8 cumulative, & already at 50, with a span of ~20 million yet to check.

Repeating George's list computation at higher precision, I get somewhat higher exponents. (Very few such exponents are primes themselves, in either list, so would be eliminated.)

We're also lucky, to be living in a time when a new Mersenne prime is discovered almost annually. There were times when it took more than a century.

[kriesel]

I predict the next discovered Mersenne prime's exponent will have a value, such that the percentage of binary digits in it that are ones, falls between 35 and 70 percent. Based on nothing more than the trend over the past few dozen.

Since only the first exponent in the list of known Mersenne primes is even, all the rest begin and end with ones in binary representation (have ones as MSB and LSB).
Of the 50 known Mersenne prime exponents, ones bits dominate overall.

bits        zeros  ones   fraction that are ones
overall     356    421    0.5418275418
interior    355    322    0.4756277696

But that is mostly at low exponents. Zeros occur more commonly in the interior bits, particularly in the higher exponents.

My picks look mostly a little too rich in ones.
80382067 (12 ones in 27 bits, 44.44...%)
113977277 (17 ones in 27 bits, 62.9629...%)
376059389 (18 ones in 29 bits, 62.069%)


It's a safe bet we won't see 100%, since for the next prime power of 2 above the currently fully tested range, 2^29-1 is divisible by 233. 2^31-1 is prime, but M2147483647 has also been factored. http://www.mersenne.ca/exponent/2147483647

[WGJC3107]

332897017

[ONeil]

83284189
June 22, 2018
My guess is based on subtraction of M50-M49, doubling the the remainder then adding it back too M50. Only reason is it landed a prime and its being tested by me as an LL.

[GP2]

83018113   9-jun-2018   moebius

[kriesel]

Originally Posted by kriesel

Ok, just for fun:

    Ballpark    Basis of ballpark                        Guess exp        Date guess                
51a    80,381,917    ratio of previous two, go up to the next unassigned/expired    80382067         Jun 14, 2018    Flag Day in the US            
51b    113,977,250    Approx expected ratio 1.47576*p50?                113977277         Aug 26, 2022    Assuming 8 million/year first test range progress        
51c    376,059,344    A long stride, 521/107*p50?                         376059389         Nov 30, 2052    "

The 8 million per year assumption is based on exponents getting harder as we go up, canceled out by computers getting faster with time, and the number of participants and systems per participant not changing much, but no major breakthroughs in number theory or revelations by ET. (Confirming or disproving a list of a select set of candidates would be way faster than exhaustive search of a great many candidates in a range.)

It's not looking good for my 51a guess. Only off by 5 days though on date of the first primality test reported. https://www.mersenne.org/report_exponent/?exp_lo=80382067&exp_hi=&full=1

[tServo]

92111179 Dec 24, 2019