[CODE]for(i=1,#mersenne,print((log(mersenne[i])/log(2^exp(-Euler)))))[/CODE]

I know extra parentheses I was thinking of doing something else but it looks cool to me. For the purposes of this code Mersenne is a vector containing all Mersenne prime exponents up to 20996011.

[QUOTE=CRGreathouse;243394]Would you quantify what would qualify as a "close match" and how many of these you'd expect to see? (I'd be happy to rate the likelihood of those in the Lenstra-Pomerance-Wagstaff model.) Ideally we'd find a situation that (1) will occur soon, say by 2020, (2) is rated as extremely likely by one model and extremely unlikely by the other.[/QUOTE]

I'm in the process of coming back to speed after a several months long
layoff from my monograph and my mersenne-related math work. I'm also
getting my programming skills out of mothballs after a recent port to a
new Windows 7 computer (32-bit). I intend to convert my MPA calculator
from 8-bit byte arithmetic to 16-bit, and eventually overhaul my LL-tester
written in C based on a port-to-C of the F90 Fortran implementation.
This will take some time. It wouldn't be fair to me to put out a best
guess at this time just to demonstrate that my YJ-Conjecture has merit.

That's fine -- but know that everyone is going to consider Eberhart's conjecture as dead as Gillies' conjecture, and if you can't even say what it would predict let alone why it should be preferred to current understanding no one is likely to be swayed.

[QUOTE=CRGreathouse;243403]That's fine -- but know that everyone is going to consider Eberhart's conjecture as dead as Gillies' conjecture, and if you can't even say what it would predict let alone why it should be preferred to current understanding no one is likely to be swayed.[/QUOTE]

OK, I'll give a seat of the pants guess -- because 1.47 < 1.500, the
current run of MPs in the <55M range will continue a few more, then
there will be two large gaps that result in approximately 3.75 to 5.25 combined multiplication.

Hence I'm guessing one gap to an M.prime between 60M and 100M
and another gap to something like 289M.

Just a guess.

I despair.

Have you ever placed a bet in your life?

[QUOTE=davieddy;243416]I despair.

Have you ever placed a bet in your life?[/QUOTE]

yep tons just non that involve money that I know of that have ever went through.

[QUOTE=science_man_88;243418]yep tons just non that involve money that I know of that have ever went through.[/QUOTE]

Perhaps that's just as well.
Thank goodness sm is on board.

All will shortly become clear:smile:

David

[QUOTE=davieddy;243416]Have you ever placed a bet in your life?[/QUOTE]Isn't that what life insurance is?

Client: I bet ya I will die.
Company: No you won't, don't be silly.
Client: Okay then, put ya money where ya mouth is.
Company: We bet lotsa$$$ you won't die.
Client: Okay. But I would like to pay my side in instalments.
Company: Deal.

[CODE](09:25)>for(n=1,38,print((2^exp(-Euler)^n)*mersenne[n]))
2.951522794210744811580555585
3.732647451136147112923117123
5.652624091595423913486847854
7.499160659926388452557214696
13.51260862628406115594039746
17.37317156076683531197685816
19.23305479274055312412830152
31.21292259396802143806030194
61.23488533202630261797025346
89.19225087685145727757649970
107.1297104549303107841899723
127.0864167560757836574724083
521.1990149045652760585791298
607.1301723129771974129946941
1279.153992112510370458632230
2203.148918751445502506628389
2281.086570945207966176713709
3217.068550833968945381727728
4253.050883087669467200087755
4423.029710659789446310603144
9689.036541981641545918633468
9941.021050444736858408209364
11213.01333126140280804013246
19937.01330845191026120986280
21701.00813328210196414014337
23209.00488383410989157481572
44497.00525718922095489042734
86243.00572091035960195646247
110503.0041156058122656445726
132049.0027612977448149239970
216091.0025370745025050669356
756839.0049890569953106188890
859433.0031808662551289143128
1257787.002613719070524895729
1398269.001631401870485101671
2976221.001949637299859489213
3021377.001111250550157048639
6972593.001439858476794543358[/CODE]

though to be a fair test of the conjecture I should make a vector of the Ceil() or floor() values of the previous calculation and see if they match up.

[url]http://mathworld.wolfram.com/images/equations/WagstaffsConjecture/NumberedEquation1.gif[/url] is the equation I used.

You need parentheses to get the right order of operations here.

You want to divide the result by mersenne[i], not multiply. The conjecture says that this quantity tends to 1.