[QUOTE=davar55;419800]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 ?[/QUOTE]

[QUOTE=LaurV;419817]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:[/QUOTE]

Of course Mn refers to the nth Mersenne exponent here.

I'm just asking someone to double check my conjecture's extension
beyond M1 thru M39 where I discovered it, to M40 thru M48.

[QUOTE=davar55;419836]Of course Mn refers to the nth Mersenne exponent here.[/QUOTE]
Ok. Then we have the mersenne numbers being [TEX]2^{M_1}-1,\ 2^{M_2}-1,\ 2^{M_3}-1[/TEX]etc. Clear. :razz:

Then what can't you check how much 57885161/43112609 is? Don't you have windows calculator?

[QUOTE=LaurV;419842]Ok. Then we have the mersenne numbers being [TEX]2^{M_1}-1,\ 2^{M_2}-1,\ 2^{M_3}-1[/TEX]etc. Clear. :razz:
Then what can't you check how much 57885161/43112609 is? Don't you have windows calculator?[/QUOTE]

I'm suggesting a list for 2 through 48 of the consecutive ratios of'
Mersenne exponents to see whether the KY conjecture of this thread
leads towards 1.5000 or the other value 1.47... from Wagstaff.

Need a loop over the M exponents.

Then make it. What's so difficult?
[CODE]
gp > \r mprimes.gph
gp > m=MERSENNE_EXPONENTS
%1 = [2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243
, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 371
56667, 42643801, 43112609, 57885161, 0]
gp > for(i=1,47,print(1.0*m[i+1]/m[i]))
1.500000000000000000000000000
1.666666666666666666666666667
1.400000000000000000000000000
1.857142857142857142857142857
1.307692307692307692307692308
1.117647058823529411764705882
1.631578947368421052631578947
1.967741935483870967741935484
1.459016393442622950819672131
1.202247191011235955056179775
1.186915887850467289719626168
4.102362204724409448818897638
1.165067178502879078694817658
2.107084019769357495881383855
1.722439405785770132916340891
1.035406264185201997276441217
1.410346339324857518632178869
1.322039166925707180603046317
1.039971784622619327533505761
2.190594619036852814831562288
1.026008876044999483950872123
1.127954934111256412835730812
1.778025506108980647462766432
1.088478707929979435220945980
1.069489885258743836689553477
1.917230384764531000904821406
1.938175607344315347102051824
1.281298192317057616270305996
1.194981131733980072939196221
1.636445561874758612333300517
3.502408707442697752335821483
1.135555910834404675234759308
1.463507917429281863740396285
1.111689817115298536238647720
2.128503885876036728269024058
1.015172260393297406341800559
2.307753385294188709320286744
1.931407297113139975329120745
1.559080745800987709362135372
1.144816651124825568056713249
1.080226378266827693437124570
1.170903692442939715156789628
1.071711309385290800674432333
1.140381737437803184681961327
1.147675624404094156238502232
1.010993579113644208216805064
1.342650383325212352608954842
gp >[/CODE]

[CODE]a=matrix(44,44,m,n,MeVec[m]/MeVec[n]);print(a)[/CODE]

now just find MeVec in the PARI command thread and add to it.

That alone doesn't show much, I agree.
But to check the KY-conjecture's value,
we need n, (Mn) ^ (1.0/n) for n from 1 to 48
to see whether, among other things,
this tends toward 1.5000 or thereabouts.

If it tends toward Wagstaff's 1.47... as n grows,
then only part of the KY may be true. If it tends
toward 1.500, the whole KY may be valid.

I know C and not pari and my compiler is not
currently available.

[QUOTE=davar55;419848]That alone doesn't show much, I agree.
But to check the KY-conjecture's value,
we need n, (Mn) ^ (1.0/n) for n from 1 to 48
to see whether, among other things,
this tends toward 1.5000 or thereabouts.

If it tends toward Wagstaff's 1.47... as n grows,
then only part of the KY may be true. If it tends
toward 1.500, the whole KY may be valid.

I know C and not pari and my compiler is not
currently available.[/QUOTE]

GP2C ?

[QUOTE=science_man_88;419850]GP2C ?[/QUOTE]

no comprendi gp2c.

[QUOTE=davar55;419882]no comprendi gp2c.[/QUOTE]

[url]http://pari.math.u-bordeaux.fr/pub/pari/manuals/gp2c/gp2c.html[/url]

It has the nice advantage of requiring both a PARI/GP installation and a C compiler.

Alright, if no one wants to help me confirm my conjecture, so be it.