Challenge

[10metreh]

Originally Posted by science_man_88

also it might tell us which ones have a digit number divisible by 3 if you look though 31 doesn't work for this case ( no surprise for me there) both of the other ones shown that are halfway between the 4 x th odd primes according to wikipedia have digit numbers divisible by 3.

Once more, base 10 seems to rule in your world.

[science_man_88]

# p Digits in Mp digits/3 ratios of digits over 3
1 2 1 0.333333333
2 3 1 0.333333333 1
3 5 2 0.666666667 2
4 7 3 1 1.5
5 13 4 1.333333333 1.333333333
6 17 6 2 1.5
7 19 6 2 1
8 31 10 3.333333333 1.666666667
9 61 19 6.333333333 1.9
10 89 27 9 1.421052632
11 107 33 11 1.222222222
12 127 39 13 1.181818182
13 521 157 52.33333333 4.025641026
14 607 183 61 1.165605096
15 1,279 386 128.6666667 2.109289617
16 2,203 664 221.3333333 1.720207254
17 2,281 687 229 1.034638554
18 3,217 969 323 1.410480349
19 4,253 1,281 427 1.321981424
20 4,423 1,332 444 1.039812646
21 9,689 2,917 972.3333333 2.18993994
22 9,941 2,993 997.6666667 1.026054165
23 11,213 3,376 1125.333333 1.127965252
24 19,937 6,002 2000.666667 1.777843602
25 21,701 6,533 2177.666667 1.08847051
26 23,209 6,987 2329 1.069493341
27 44,497 13,395 4465 1.917131816
28 86,243 25,962 8654 1.93818589
29 110,503 33,265 11088.33333 1.28129574
30 132,049 39,751 13250.33333 1.194979708
31 216,091 65,050 21683.33333 1.636436819
32 756,839 227,832 75944 3.502413528
33 859,433 258,716 86238.66667 1.135556024
34 1,257,787 378,632 126210.6667 1.463504383
35 1,398,269 420,921 140307 1.111688922
36 2,976,221 895,932 298644 2.128503924
37 3,021,377 909,526 303175.3333 1.015173027
38 6,972,593 2,098,960 699653.3333 2.30775151
39 13,466,917 4,053,946 1351315.333 1.931406983
40[*] 20,996,011 6,320,430 2106810 1.559080955
41[*] 24,036,583 7,235,733 2411911 1.144816571
42[*] 25,964,951 7,816,230 2605410 1.080226426
43[*] 30,402,457 9,152,052 3050684 1.17090362
44[*] 32,582,657 9,808,358 3269452.667 1.07171135
45[*] 37,156,667 11,185,272 3728424 1.140381703
46[*] 42,643,801 12,837,064 4279021.333 1.147675622
47[*] 43,112,609 12,978,189 4326063 1.010993557

[Dougal]

and again,what does this tell us?this is just spamming the forum with pointless posts.

[science_man_88]

It shows the divisibility of 3 of the mersenne primes digit count

[Dougal]

and what use is that information?

[science_man_88]

For one most are, so maybe we can look for prime exponents that will give us digit lengths that divide by 3 which we could look at the exponent figure a pattern for base 10 length then say well is it divisible by 3 if it is then it may actually worth checking for it

[science_man_88]

so if we know that certain exponent ( like 607) will have digit lengths dividable by 3 then we might find one like it by the first pattern then say the other stuff I said and find them)

[Dougal]

yes,but every third number is divisable by three,and the fact that they arent all evenly divisable by 3 means that this information is useless.

[science_man_88]

log2(3) = 1.584962500721156............................

so if the prime exponent is not modulo 0 by this maybe it's 2^p-1 digit length is not divisible by 3 and hence is less likely to be a mersenne prime

[science_man_88]

eg. 19/ log2(3) gives just under 12 ( probably because the value I use was rounded) so 2^19-1 is likely to be a mersenne prime if I'm not mistaken and this example is.

[science_man_88]

another one that if you round up will work is the 47th one listed above