[QUOTE=davar55;349782]I'm sure you're prepared to show that the YJ version is
heuristically not as strong as Wagstaff?[/QUOTE]

I would certainly say that your conjecture is not as sound as the Wagstaff conjecture! There's a strong heuristic there, and none at all that I can see for yours. There's [i]numerical[/i] evidence, which isn't strong enough to distinguish between the two, but no [i]heuristics[/i] you've provided.

[QUOTE=CRGreathouse;354845]I would certainly say that your conjecture is not as sound as the Wagstaff conjecture! There's a strong heuristic there, and none at all that I can see for yours. There's [i]numerical[/i] evidence, which isn't strong enough to distinguish between the two, but no [i]heuristics[/i] you've provided.[/QUOTE]

OK. Granted.

Note:

1.500000 ^ 48 ~= 283387333.

1.470000 ^ 48 ~= 107456345.

M48* = 57885161.

So using YJEbKY, it's under by a factor of ~5.

Using Wag, it's under by a factor of ~2.

ATM, Wag is considerably closer.

My overdue apologies to two forumites jiny** and **motl.

I seven years ago misapplied their interest in this conjecture
and attributed to them a belief in its veracity that I now believe
they did not have.

I believe it is necessary to make up for one's own mistakes.
I've made a few big ones on this forum, and this is the only way
for me to acknowledge that.

[QUOTE=davar55;363464]My overdue apologies to two forumites jiny** and **motl.

I seven years ago misapplied their interest in this conjecture
and attributed to them a belief in its veracity that I now believe
they did not have.

I believe it is necessary to make up for one's own mistakes.
I've made a few big ones on this forum, and this is the only way
for me to acknowledge that.[/QUOTE]

That was jinydu and _motl. Sorry about that.

By the way, has Wagstaff Conjecture been proven yet?

[QUOTE=davar55;401050]By the way, has Wagstaff Conjecture been proven yet?[/QUOTE]

No. It's unlikely to be proved in the near future.

[QUOTE=CRGreathouse;401075]No. It's unlikely to be proved in the near future.[/QUOTE]

And why is that? And exactly how unlikely?

Has anyone tried contesting this conjecture based on M40 thru M48?

Could someone please compute
R[sub]n[/sub] = (M[sub]n+1[/sub] / M[sub]n[/sub])
for n from 1 through 47 and compare this sequence of ratios
to 1.5000 versus say 1.47
and see if we might guess at decent bounds on a guess
for the next few values M49, M50, and M51 ?

I think you mean exponents' ratios and not mersenne's ratios, which are powers of two...
Different "numerologists" did this repeatedly, with no utility for the reality.
[URL="https://primes.utm.edu/notes/faq/NextMersenne.html"]This graphic[/URL] is "linear" we know that, but from here to predictions... well... :whistle: