[QUOTE=CRGreathouse;250696]So where's the next Mersenne prime going to be?[/QUOTE]

I'm not talking about the exponents I'm saying that the nth number in the number spiral can be found in this part of the number spiral I'm not sure but if they have to line up exponent wise each one can only link to 8 directions, almost like a 5 queens problem, which unfortunately can cover a whole chessboard last i checked so it all depends on where the last ones are and how far you check I'll see what I find in the paths lol.

[QUOTE=science_man_88;250699]I'm not talking about the exponents I'm saying that the nth number in the number spiral can be found in this part of the number spiral I'm not sure but if they have to line up exponent wise each one can only link to 8 directions, almost like a 5 queens problem, which unfortunately can cover a whole chessboard last i checked so it all depends on where the last ones are and how far you check I'll see what I find in the paths lol.[/QUOTE]

So where's the next Mersenne prime going to be?

[QUOTE=ewmayer;250704]So where's the next Mersenne prime going to be?[/QUOTE]

well as far as I can tell they line up in some way with at least one more as for how to find out how they link up. I'm not sure. I know a way knowing the exponent what round and row /column it will possibly land as for telling if they all line up so far or which ones would have loose ends but as I've said,I'm not sure as of yet how to find that out without creating the number spiral itself and plotting them all. I was thinking of trying to find a pattern to which ones link up by plotting it on a scatter plot maybe. anyone else have ways to forward this if it can be used ?

heres a list of squares certain ones are on:

[CODE]2 [COLOR="red"]FC[/COLOR][COLOR="Red"]218[/COLOR]
3 [COLOR="red"]FC[/COLOR][COLOR="red"]217[/COLOR]
5 [COLOR="red"]FA[/COLOR][COLOR="red"]217[/COLOR]
7 [COLOR="Red"]FA[/COLOR]219
13 FD[COLOR="red"]216[/COLOR]
17 [COLOR="red"]EZ[/COLOR][COLOR="red"]216[/COLOR]
19 [COLOR="red"]EZ[/COLOR][COLOR="red"]218[/COLOR]
31 [COLOR="red"]FE[/COLOR]215
61 [COLOR="red"]FB[/COLOR]214
127 FH[COLOR="red"]218[/COLOR]
521 [COLOR="red"]FE[/COLOR]229
607 EV230
1279 [COLOR="red"]FB[/COLOR][COLOR="red"]200[/COLOR]
2203 FS241
2281 [COLOR="red"]FB[/COLOR]194
3217 EX[COLOR="red"]246[/COLOR]
4253 GI223
4423 DU251
9689 DE253
9941 FL168
11213 DY165
19937 HU233
21701 HX[COLOR="red"]200[/COLOR]
23209 CD[COLOR="Red"]246[/COLOR]
[/CODE]

the red are the easy relationships to find the harder ones are on the 45 degree diagonals, in other words the one down one over type.

[CODE]2 [COLOR="red"]FC[/COLOR][COLOR="Red"]218[/COLOR]
[COLOR="lime"]3 [/COLOR] [COLOR="red"]FC[/COLOR][COLOR="red"]217[/COLOR]
[COLOR="Lime"]5 [/COLOR] [COLOR="red"]FA[/COLOR][COLOR="red"]217[/COLOR]
[COLOR="lime"]7 [/COLOR] [COLOR="Red"]FA[/COLOR]219
[COLOR="Lime"]13 [/COLOR] FD[COLOR="red"]216[/COLOR]
[COLOR="lime"]17[/COLOR] [COLOR="red"]EZ[/COLOR][COLOR="red"]216[/COLOR]
[COLOR="lime"]19[/COLOR] [COLOR="red"]EZ[/COLOR][COLOR="red"]218[/COLOR]
[COLOR="lime"]31[/COLOR] [COLOR="red"]FE[/COLOR]215
[COLOR="lime"]61 [/COLOR] [COLOR="red"]FB[/COLOR]214
[COLOR="lime"]127[/COLOR] FH[COLOR="red"]218[/COLOR]
521 [COLOR="red"]FE[/COLOR]229
[COLOR="lime"]607[/COLOR] EV230
1279 [COLOR="red"]FB[/COLOR][COLOR="red"]200[/COLOR]
[COLOR="Lime"]2203[/COLOR] FS241
2281 [COLOR="red"]FB[/COLOR]194
3217 EX[COLOR="red"]246[/COLOR]
4253 GI223
[COLOR="Lime"]4423[/COLOR] DU251
9689 DE253
9941 FL168
[COLOR="Lime"]11213[/COLOR] DY165
19937 HU233
21701 HX[COLOR="red"]200[/COLOR]
23209 CD[COLOR="Red"]246[/COLOR]
[/CODE]

the green are diagonals that I have easily found.

I don't understand your charts, but you seem to be suggesting that you know where some Mersenne prime-generating exponents are (though your patterns don't account for all of them). So... what are they? :smile:

[QUOTE=CRGreathouse;250735]I don't understand your charts, but you seem to be suggesting that you know where some Mersenne prime-generating exponents are (though your patterns don't account for all of them). So... what are they? :smile:[/QUOTE]



[COLOR="red"]5[/COLOR][COLOR="DarkOrange"] 4[/COLOR][COLOR="red"] 3[/COLOR]
[COLOR="DarkOrange"]6[/COLOR] [COLOR="DarkOrange"]1[/COLOR] [COLOR="Red"]2[/COLOR]
[COLOR="red"]7[/COLOR] 8 9

the red are the exponents the orange are connecting them 3 has a line to 5 and 2(if you count 0 as a length or you count the other exponent square) has a linear connection with 3 and 5 has a linear connection with 7 and 3 has a diagonal relation with 7 the file I uploaded ( which could hold a sign of decompression bomb goes to about 11213 and just highlights the mersenne exponents and a few other things like superperfect numbers. so far without expanding it any more my current one is up to over 27000 and if you look I don't have a connection known for 4 out of 26 but that's still 85% that do so far I'm confident if I expanded I'd find something to match them up with but I'd rather calculate which lined up than expand my number spiral to over 43 million or even 20 million as each round is only about 5-8 hundred it may take a while.

[QUOTE=science_man_88;250778]my current one is up to over 27000 and if you look I don't have a connection known for 4 out of 26 but that's still 85% that do so far[/QUOTE]
But, have you also run the experiment the other way around, i.e. checked whether your magic foo-formula produces any false positives? Anyone (well, maybe not anyone, but most people reading this) can back-fit known data. I can take any finite set of n known M-prime exponents and curve-fit them exactly with a suitably high-order polynomial p(x) such that the values p(1), p(2), etc exactly match the 1st, 2nd, etc M-prime exponents. Once I do, the obvious next step is to see what p(n+1) predicts.
[QUOTE]I'm confident if I expanded I'd find something to match them up with but I'd rather calculate which lined up than expand my number spiral to over 43 million or even 20 million as each round is only about 5-8 hundred it may take a while.[/QUOTE]
That should give you time to fix the comma and semicolon keys on your keyboard, then.

[QUOTE=ewmayer;250847]But, have you also run the experiment the other way around, i.e. checked whether your magic foo-formula produces any false positives? Anyone (well, maybe not anyone, but most people reading this) can back-fit known data. I can take any finite set of n known M-prime exponents and curve-fit them exactly with a suitably high-order polynomial p(x) such that the values p(1), p(2), etc exactly match the 1st, 2nd, etc M-prime exponents. Once I do, the obvious next step is to see what p(n+1) predicts.

That should give you time to fix the comma and semicolon keys on your keyboard, then.[/QUOTE]

Well p1 "is on a diagonal with" p2 implies p2 "is on a diagonal with" p1 unless you use the term ante-diagonal. It's a symmetric binary relation, However it's not a transitive relation. It's not a magic formula, It's just something I found that looked cool. the only formula I've tried to find is a formula to tell where a number would be in the number spiral.

Want a quick run through of my idea with triangular numbers ? It goes as such:

lets say we use 3 as an example:

3-1 = 2 = 1 + 1 ( largest sum of 2 triangular numbers that is less than or equal to P-1) since it would be congruent to 0 mod (the sum of those triangular numbers) we can take it that 3 is on the same diagonal as 1.Knowing something like this could help pinpoint where 2 numbers are in relation to each other ( proving if they are in a diagonal together or not). Even negative moduli could be useful for certain diagonals and if they are equal to .5* next integer to use in for 2 numbers assuming they are on the same or directly opposing sides they are likely in a line with each other. Anyone want to see it in a bigger, or more complicated example ?

To expand it going to 5 we get 5-1 = 4 = 1 +3 which means since both 1 and 3 are triangular 5 is on a diagonal with 1 if you break it to the next corner around a number spiral after the original number you get the amount of squares: 1,1,2,2,3,3,4,4,5,5 . This is why the formula can tell you were it is because mod the sum of triangular numbers. tells you where in relation to a specific corner the number is and,the fact that given enough numbers you can cover any square eventually. 3 and 13 are both at the top right corner in their specific parts of the spiral so they are on the same diagonal.