new candidates for M...46 and M48

[cochet]

May I inflict to you some new predictions ?
Well.

1) 43112609 is not M46 but M47
2) the genuine M46 is into the bracket 39336867-39473371
3) M48 is probably into the bracket 44494541-45372809

You'll find all details here :

http://home.tele2.fr/lacanmaths/reglesnew1.html


*remember that the interval I proposed for M45 was the good one !

[davieddy]

How much luckier do you expect GIMPS to get?
Perlease...

[TimSorbet]

Why are some of the cells in your spreadsheet colored different?
Under Rule 4:

What about M23 (2^11213-1)?
With M23 as Mz, b-a=1221, while d +/- c +/- 2*e = 5163, 5195, 5337, or 5369
There's no equality, so I guess M11213 isn't in the range to be a candidate for M23, huh?

Or M22 (2^9941-1)?
With M22 as Mz, b-a=244, while d +/- c +/- 2*e = -172, 176, 164, or 512
There's no equality, so I guess M9941 isn't in the range to be a candidate for M22, huh?


Under Rule 3:

With M23 as Mz, a +/- b = 1221 or 1323, while c +/- d = 5258 or 5274
There's no equality, so I guess M11213 isn't in the range to be a candidate for M23, huh?


If your method doesn't stand up to the earlier Mersenne primes, why would it be correct for the current ones? By the way, how exactly your method is calculated is pretty complicated, but it seems it would be effected by the following observation:

The recent primes (since M40 at p=~20M) are far closer together than heuristics projected.

If your method suggests the next primes based on how close together the recent ones have been (indirectly, I'm sure, as you'd want to check it with recent primes to see if it fits, but not necessarily go through the time to check that all 44 fit it), it will be very far off for the older primes.

[cochet]

Under Rule 3:

With M23 as Mz, a +/- b = 1221 or 1323, while c +/- d = 5258 or 5274
There's no equality, so I guess M11213 isn't in the range to be a candidate for M23, huh?

For M11213, the good formula is a + b = c +d = 5184 , and the bracket is 10193-15125 , with a gap of 4932, soit Y37-Y36 on the spreadsheet.


Otherwise, it's true that the member "2e", on the rule IVb, is from recent apparition (around M38).
I can nothing if there is a "resserrement" of the last values in the sequence.

[cochet]

It’s necessary to be more precise. So, here are the last results obtained with the rule III :

-M37
a – b = c – d = - 1039116 and the interval is 2835739-3116703

-M38
a – b = c + d = 1673278 4694655- +infinite

-M39
a – b = c – d + 2e = 5484012 12456605-14829870
(the value e is under the value d into the column)

-M40
a + b = c – d + 2e = 7674480 19961241-21141397

-M41
a + b = c – d = 4985986 16010025-25981997

-M42
a + b = c + d – 2e = 2005802 22030781-26042385

-M43
a + b = c + d = 6416890 29005523-32381841 (gap AS 56 on the spreadsheet)

-M44
a + b = c + d = 3325302 32330825-33727759 (gap AT57)

-M45
a + b = c + d = 4689338 37020163-37271995 (gap AU58)


-for M46 now, two possibilities :
1) the most vraisemblable
a + b = c + d = 2316704 39336867-39473371 (gap AV59)

2) a + b = c – d + 2e = 6831316 41730677-43987583
It’s the interval of 43112609, but I do not believe in this result, because the top of the column 46 not matches with the others in this case.


Take a look here to see "how to reduce the intervals" :
http://home.tele2.fr/lacanmaths/reglesnew1.html

Alain