How unlucky?
 

I know we are dealing with large k values, but have we been inordinately unlucky in not finding a single factor yet?

Unlucky?! I found 20! :devil:
The source works! :bow:

But seriously unlucky for Fermats, I agree.

We don't see how luck plays in at all. It is what it is. (Right?)

[B][SIZE=3]Definition of [I]LUCK[/I][/SIZE][/B]

[I]a[/I] [B]:[/B] a force that brings good fortune or adversity
[I]b[/I] [B]:[/B] the events or circumstances that operate for or against an individual

I also say it works. It finds all (findable) known factors, why it should be missing unknown factors? (if this was the question, but I smell here the question is more about math, if you are in fact asking about expectancy to find any factor, like "were we unlucky, or the expectancy is really so low?", well, it is quite low too, for the ranges we are testing, only very few factors should be expected). I just think there are pure and simple no factors in the ranges we tested, except one factor which managed to stay hidden, but hiding is bad because now he is cornered somewhere and can't get out and I will put my paw on it soon... :razz:

[QUOTE=Prime95;314338]I know we are dealing with large k values, but have we been inordinately unlucky in not finding a single factor yet?[/QUOTE]

Well it would of course always be a good idea to try mmff against some known factors (if any) just to make sure everything works, if not done already. MM31 have composits within reach I think.

I did quite some work for OBD and I thought for awhile that I was unfortunate, but then I found 2 factors so now I am more fortunate then I should be according to statistics I think.

Someone could maybe do a little statistics here?

[QUOTE=LaurV;314355] if you are in fact asking about expectancy to find any factor, like "were we unlucky, or the expectancy is really so low?",[/QUOTE]

Yes, it was a math question. With frmky churning out tons of work and several others contributing, I was wondering if the expected number of factors found was less than 1? 1 to 2? above 2? I guess I'm too lazy to go back through the posted results to come up with an exact figure.

[QUOTE=ET_;313955]In one month of work with mmff, the 22% of the equivalent work done since 2001 has been completed.[/QUOTE]

Sounds unlucky to me.

I don't know how to calculate the odds of factors within a certain k range, but here is the completed ranges from results thread up to Batalov "N=25 to 2e15" Oct 13th (excluding the few fermat results with version 0.20).
If someone knows the formula for the odds, I'll be happy to try to calculate it.

[CODE]Fermat:
n k
25 500T-2000T
28 550T-1000T
29 550T-1000T
33 700T-1000T
34 700T-1000T
37 4500T-5000T
40 600T-1000T
41 600T-1000T
42 600T-1000T
43 600T-1000T
44 400T-700T
45 500T-1000T
50 300T-1000T
51 350T-1000T
52 300T-1000T
53 200T-1000T
54 200T-1000T
55 200T-1000T
56 200T-1000T
57 280T-1000T
58 280T-1000T
60 200T-1500T
61 200T-1000T
62 200T-1000T
63 200T-1000T
71 300T-1000T
72 300T-1000T
73 300T-1000T
74 300T-1000T
83 35T-281T
84 35T-281T
85 35T-281T
86 25T-281T
87 25T-281T
88 25T-281T
89 25T-281T
90 100T-1000T
100 4T-100T
101 16T-100T
102 16T-100T
103 16T-100T
104 16T-100T
105 16T-100T
106 16T-100T
107 16T-100T
108 16T-100T
109 16T-100T
110 30T-100T
111 30T-100T
112 30T-100T
113 30T-100T
114 30T-100T
115 30T-100T
116 30T-100T
117 30T-100T
118 30T-100T
119 30T-100T
120 30T-100T
121 30T-100T
122 30T-100T
123 30T-100T
124 30T-100T
125 30T-100T
126 30T-100T
127 30T-100T
128 30T-100T
129 30T-100T
130 12T-50T
131 12T-50T
132 12T-50T
133 12T-50T
134 12T-50T
135 12T-50T
136 12T-50T
137 12T-50T
138 12T-50T
139 12T-50T

k
MM31 18000T-25000T
MM61 3573T-10000T
MM89 7T-1300T
MM107 4T-1000T
MM127 563T-3700T and 4000T-4600T and 5500T-5800T
[/CODE]

It should be the probability of f=k*2[SUP]N[/SUP]+1 being prime (which is C/ln f) times probability of dividing a Fermat number which is 1/k, then sum (intergrate is fine) over the range. There's [URL="http://www.ams.org/journals/mcom/1998-67-221/S0025-5718-98-00891-6/S0025-5718-98-00891-6.pdf"]Bjorn/Riesel[/URL] (1998) with a detailed treatment:

I think it's more unlucky that we haven't found a new Mersenne prime since April 2009.

[QUOTE=ixfd64;314569]I think it's more unlucky that we haven't found a new Mersenne prime since April 2009.[/QUOTE]

Well, between M[10,000,000 digits] and M[100,000,000 digits] we are supposed to find 6 Mersenne primes according to the theory (about 6 between M[10[SUP]n[/SUP] digits] and M[10[SUP]n+1[/SUP] digits]) so I would say we have been extremely lucky that have found 3 already.

In your screenshot they have the number of primes k*2[sup]n[/sup]+1 for k<K is G(K)=K/(ln(K*2[sup]n[/sup])-1).

So trying this for example on n=25 and 500T<k<2000T

G(2000T)-G(500T) = 2.88*10[sup]13[/sup] primes

Now each of these you say has a 1/k chance of dividing a fermat number, so if we divide the number of primes with the average k in the interval which is 1250T it should be an ok estimate?

2.88*10[sup]13[/sup]/1250*10[sup]12[/sup] = 0.0231, so 2.31% chance of finding a fermat factor in that interval.

Doing this for all the ranges gives expected fermat factors in the ranges done so far at 0.95, unless my calculations are all wrong?

[CODE]Fermat:
n k
25 500T-2000T 0.02305923714
28 550T-1000T 0.01081348535
29 550T-1000T 0.01067572583
33 700T-1000T 0.006163534161
34 700T-1000T 0.006089842254
37 4500T-5000T 0.001704400774
40 600T-1000T 0.008058379498
41 600T-1000T 0.00796937526
42 600T-1000T 0.007882315112
43 600T-1000T 0.007797136063
44 400T-700T 0.008464224672
45 500T-1000T 0.0101876489
50 300T-1000T 0.01566992576
51 350T-1000T 0.01386193619
52 300T-1000T 0.01536014979
53 200T-1000T 0.01886175148
54 200T-1000T 0.01867863009
55 200T-1000T 0.01849902961
56 200T-1000T 0.01832284948
57 280T-1000T 0.01529457624
58 280T-1000T 0.01515181805
60 200T-1500T 0.02016286432
61 200T-1000T 0.01748999027
62 200T-1000T 0.01733242097
63 200T-1000T 0.01717766503
71 300T-1000T 0.01293148238
72 300T-1000T 0.01282475399
73 300T-1000T 0.01271977269
74 300T-1000T 0.01261649593
83 35T-281T 0.01727941477
84 35T-281T 0.01714751685
85 35T-281T 0.01701761711
86 25T-281T 0.01816263451
87 25T-281T 0.01802700773
88 25T-281T 0.01789339132
89 25T-281T 0.01776174093
90 100T-1000T 0.0170126916
100 4T-100T 0.01833508944
101 16T-100T 0.01425457045
102 16T-100T 0.01415798841
103 16T-100T 0.01406270624
104 16T-100T 0.01396869789
105 16T-100T 0.01387593798
106 16T-100T 0.0137844018
107 16T-100T 0.01369406531
108 16T-100T 0.01360490506
109 16T-100T 0.01351689825
110 30T-100T 0.009970885797
111 30T-100T 0.009907309386
112 30T-100T 0.009844538526
113 30T-100T 0.009782558006
114 30T-100T 0.009721352994
115 30T-100T 0.009660909025
116 30T-100T 0.009601211995
117 30T-100T 0.009542248144
118 30T-100T 0.009484004048
119 30T-100T 0.009426466609
120 30T-100T 0.009369623046
121 30T-100T 0.009313460883
122 30T-100T 0.009257967941
123 30T-100T 0.009203132331
124 30T-100T 0.009148942443
125 30T-100T 0.009095386938
126 30T-100T 0.009042454743
127 30T-100T 0.00899013504
128 30T-100T 0.008938417258
129 30T-100T 0.008887291072
130 12T-50T 0.01012143297
131 12T-50T 0.01006383816
132 12T-50T 0.01000689509
133 12T-50T 0.009950592732
134 12T-50T 0.009894920352
135 12T-50T 0.00983986743
136 12T-50T 0.009785423686
137 12T-50T 0.009731579065
138 12T-50T 0.009678323732
139 12T-50T 0.009625648066
--------------------------------------
Total 0.9522655104[/CODE]