Problem 111

[MHealy]

Hmm... Shouldn't that be the matter with N? Just like in the description M(4,1) = 3, but N(4,1) = 9. A 4-digit prime has at most 3 consecutive 1s, and 9 primes having 4 digits contain 3 repeated 1s. So I figured M() is about the maximum number of consecutive digits d.

No, whether the digits are consecutive is completely irrelevant. If the only primes in the example were 1151, 1171, 1181, 1511 and 1811, M(4,1) would still be 3.

[Oliver1978]

Ok. Which also bothers me is -from the table- N(10,0)=8. Since M(10,0)=9 there should be 8 primes with 10 digits containing 9 zeros. Is that right? The only 10-digit primes with 8 zeros I could find are 1000000007 and ...9.

[MHealy]

Ok. Which also bothers me is -from the table- N(10,0)=8. Since M(10,0)=8 there should be 8 primes with 10 digits containing 8 zeros. Is that right? The only 10-digit primes with 8 zeros I could find are 1000000007 and ...9.

Yes, there are eight of them. I assume the other values for N(10,d) which harryh did not say were wrong are also correct.

[Oliver1978]

Thanks a lot for clearing this! I guess I wasn't the only one who took "consecutiv" for "repeated".

[Oliver1978]

Finally owned this one. For those who are still seeking, OPs table proved a valuable asset for debugging. N(10, 2) and N(10, 8) are indeed incorrect. But once you have the others you will easily find N() for d = 2 and 8.

[RishadanPort]

I might be missing something...

But why doesn't the question just ask: "What is the sum of all 10 digit primes"... end of question.

[DJohn]

I might be missing something...

But why doesn't the question just ask: "What is the sum of all 10 digit primes"... end of question.

Simply because the solution is not the sum of all 10 digit primes.

For 4 digit numbers, 1013 is prime, but we don't include it in S(4, 1) because it only has 2 1s and M(4, 1) is 3. It won't be included in S(4, 0) or S(4, 3), because it doesn't have enough of those digits either.

[RishadanPort]

Ah!

Oops

Also

I am assuming the same prime can be in 2 or more categories, and have it's sum added in multiple times?

[DJohn]

I am assuming the same prime can be in 2 or more categories, and have it's sum added in multiple times?

It doesn't happen in the case of 4 digit primes, but there's nothing in the problem statement that rules it out. Each S() is evaluated independently.

[oms1953]

I have the following as solution to Problem 111.

Code: Select all

| D | M | N  |       S      |
Snipped by moderator
Please don't post (partial) solutions

This is short of what the answer should be.
I think I generated all the prime 10-digit combinations.
I used Julia and used Julia's Combinatorics and Primes Package.

[SaxTenor]

What exactly is your question?

[hk]

@Saxtenor:
Question falls outside what we allow.
See the pink box.

[oms1953]

What exactly is your question?

I'm wrong and the question is how do I do it right? Any tip on how to do it right or where I can find resources to possible solutions will be appreciated.

[Oliver1012]

Greetings, another evening, another pushed topic

I have to go through all of the problems again due to a system failure with irrecoverable files holding the data. Anyways... dealing with #111 I've come across a problem. Would it be possible if someone verified my findings?

For 7-digit primes I get M(7, 2) = 5 with S(7, 2) = 117535528.
For 6-digit primes I get M(6, 7) = 5 with S(7, 7) = 8510217.
Furthermore, S(8, d) with 0 $\le$ d $\le$ 9 ends with 51254.

Could this be correct? Any help is appreciated. Thanks!

[SAG145]

Your results for 6 and 7 digit primes are correct.
But for 8 digit primes the sum should end with 30042.
Also, I believe you have a typo - you wrote S(7,7) instead of S(6,7).

[Oliver1012]

Your results for 6 and 7 digit primes are correct.
But for 8 digit primes the sum should end with 30042.
Also, I believe you have a typo - you wrote S(7,7) instead of S(6,7).

Thank you. And yes, you are correct, I meant to say S(6, 7).

I'm still not sure where my S(8, d) might go wrong
For example, I get M(8, 1) = 7 with a total sum of 288629940, and M(8, 9) = 7 with S(8, 9) = 1099396937.

[SAG145]

S(8,1) = 266408728.
If you want you can PM me your code and I'll try to help you find the mistake.

[Oliver1012]

S(8,1) = 266408728.
If you want you can PM me your code and I'll try to help you find the mistake.

PM sent....

...and solved

[blu.knite]

I'm kinda stuck with this now. I've got it to the point where it will give me M, N and S for various d pretty quickly. The following two of my rows are different from OP's table (leaving out sums to avoid spoilers). Do these seem correct?

Code: Select all

M(10,2)=8, N(10,2)=40
M(10,8)=8, N(10,8)=34