Mersenne Memorization

[davar55]

How many Mersenne Prime exponents have YOU memorized?

It's not very likely that every electronic and printed record of the list
of exponents should be simultaneously corrupted, resulting in a loss of
a lot of work, but just in case ...

Well, just out of curiosity, how high can you reliably recite the list?

[ixfd64]

I currently know the following off the top of my head: 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 2203, 9941, 11213, 44497, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667 and 43112609.

[sylvester]

Is somebody working on casting a sequel to the Rainman?

[Batalov]

No! Fahrenheit 451 ½

[sylvester]

Originally Posted by Batalov

Fahrenheit 451

Thanks for motivating me to watch this movie. Even considering the low budget, the movie was weak. But the story was good enough to shine through a bad adaptation to the screen.

At the very least now I know what was the inspiration for the armchair of Dr.Evil in Austin Powers.

[kdq]

Originally Posted by ixfd64

I currently know the following off the top of my head: 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 2203, 9941, 11213, 44497, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667 and 43112609.

You forgot 1279, 2281, 3217, 4253, 4423, 9689, 19937, 21701, 23209, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377. No, I don't have them memorized, they're from my list:

Digits Digits
# p in Mp in Pp
-- -------- -------- --------
1 2 1 1
2 3 1 2
3 5 2 3
4 7 3 4
5 13 4 8
6 17 6 10
7 19 6 12
8 31 10 19
9 61 19 37
10 89 27 54
11 107 33 65
12 127 39 77
13 521 157 314
14 607 183 366
15 1279 386 770
16 2203 664 1327
17 2281 687 1373
18 3217 969 1937
19 4253 1281 2561
20 4423 1332 2663
21 9689 2917 5834
22 9941 2993 5985
23 11213 3376 6751
24 19937 6002 12003
25 21701 6533 13066
26 23209 6987 13973
27 44497 13395 26790
28 86243 25962 51924
29 110503 33265 66530
30 132049 39751 79502
31 216091 65050 130100
32 756839 227832 455663
33 859433 258716 517430
34 1257787 378632 757263
35 1398269 420921 841842
36 2976221 895932 1791864
37 3021377 909526 1819050
38 6972593 2098960 4197919
39 13466917 4053946 8107892
40 20996011 6320430 12640858
41 24036583 7235733 14471465
42 25964951 7816230 15632458
43 30402457 9152052 18304103
44 32582657 9808358 19616714
46* 37156667 11185272 22370543
45 43112609 12978189 25956377


Which then is followed by the actual Mersenne primes themselves. I have a similar file for the perfect numbers, and, yes, the first ten million digits of PI.

[davar55]

Has anyone ever even bothered to examine the
relationship between the decimal digits of pi and
the list of primes/Mersennes/Fermations?

There is one. A very important one. Not trivially describable.

[plandon]

Originally Posted by davar55

How many Mersenne Prime exponents have YOU memorized?

More impressive at parties is if you then recite the primes,
in binary ;)

[10metreh]

Originally Posted by davar55

Has anyone ever even bothered to examine the
relationship between the decimal digits of pi and
the list of primes/Mersennes/Fermations?

There is one. A very important one. Not trivially describable.

Don't all Mersenne primes (and all numbers) appear in Pi somewhere?

[Brian-E]

Originally Posted by davar55

Has anyone ever even bothered to examine the
relationship between the decimal digits of pi and
the list of primes/Mersennes/Fermations?

There is one. A very important one. Not trivially describable.

Not knowing what a Fermation is, I searched but only found "Fermatian" which apparently is an alternative name for a Poulet number, a Fermat pseudoprime to base 2. Is that what you meant?

[starrynte]

only know some of the low ones (below 127);
521, 607, 2203, 11213 from testing my ll midlet;
42643801, 43112609.

Just noticed, kdq your list needs to be updated with 42643801, recently discovered