## Problem 200

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Comments, questions and clarifications about PE problems.

- JamieCamardelle
**Posts:**20**Joined:**Wed May 14, 2008 5:34 am

### clarifying problem 200

Hi, thanks for keeping up such a great website. I just need to know, for problem 200, is it a valid change to turn the first digit into a zero? Just want to know because the change is drastic, creating a new number of one fewer digits than the other. Thanks.

### Re: clarifying problem 200

Yes, I think so. It's some time ago I solved this problem, but looking at my algorithm, I did turn the first digit into a zero, too.

Last edited by Tommy137 on Wed Oct 29, 2008 10:36 pm, edited 1 time in total.

### Re: clarifying problem 200

Leading zeroes are never allowed in any of the problems, including this one.

It might not make much difference here since most prime-proof numbers are even....

It might not make much difference here since most prime-proof numbers are even....

_{Jaap's Puzzle Page}

### Re: clarifying problem 200

I think he means checking if a number is prime-proof. In which case, according to my algorithm (and most of the others in the discussion), you can swap out a zero for the first digit. If this isn't intended behavior, then I guess it doesn't make a difference.

ex ~100%'er... until the gf came along.

### Re: clarifying problem 200

A string of digits that starts with a zero is strictly speaking not a number so checking whether it is prime or not does not make sense.quilan wrote:I think he means checking if a number is prime-proof. In which case, according to my algorithm (and most of the others in the discussion), you can swap out a zero for the first digit.

My program never changed the first digit to zero. I think it happens to be the case that it doesn't matter in this problem.

_{Jaap's Puzzle Page}

### Re: clarifying problem 200

You're right, of course.jaap wrote:Leading zeroes are never allowed in any of the problems

I wonder why it didn't come to my mind, when I coded my program. Obviously I just started to write it, then run it and checked the solution

- JamieCamardelle
**Posts:**20**Joined:**Wed May 14, 2008 5:34 am

### Re: clarifying problem 200

Thanks for the answers. It seems I can go about it either way.

### Problem 200

Is there any

**odd**prime-proof sqube which contains the contiguous sub-string "200"?Math and Programming are complements

### Re: Problem 200

Could somebody explain me what is this "changing a single digit to make it prime" thing?

Thx.

Thx.

### Re: Problem 200

For example 72, the following are prime numbers:

71, 73, 79

For 200 none of the following are prime numbers:

100,200,300,...,900

200,210,220,...,290

200,201,202,...,209

Thus, 72 can change one digit to make it a prime, but 200 can never change only one digit to make it a prime and thus is prime-proof.

71, 73, 79

For 200 none of the following are prime numbers:

100,200,300,...,900

200,210,220,...,290

200,201,202,...,209

Thus, 72 can change one digit to make it a prime, but 200 can never change only one digit to make it a prime and thus is prime-proof.

ex ~100%'er... until the gf came along.

- BostonBear
**Posts:**17**Joined:**Thu Apr 28, 2011 4:48 am**Location:**Saugus, MA

### Re: Problem 200

I am confused about the precise definition of "sub-string" in this problem. does that mean the sqube can NOT either Start or End with "200"?

### Re: Problem 200

The "200" can be at the start, middle, or end (or can even occur multiple times). Sub-string simply means that the three digits "2", "0", and "0" must be adjacent and in that order.BostonBear wrote:I am confused about the precise definition of "sub-string" in this problem. does that mean the sqube can NOT either Start or End with "200"?

_{Jaap's Puzzle Page}

### Re: Problem 200

I must be doing something silly with this one (

Can someone kindly check if the first few numbers satisfying the conditions are the following?

(1 200)

(2 1992008)

(3 20047112)

(4 42120027)

Thanks!

**Problem 200**(View Problem))Can someone kindly check if the first few numbers satisfying the conditions are the following?

(1 200)

(2 1992008)

(3 20047112)

(4 42120027)

Thanks!

Last edited by olopierpa on Fri May 25, 2012 3:56 pm, edited 1 time in total.

### Re: Problem 200

That's a lot of results to post in a forum with a dancing header that says "In particular don't post any code fragments or results".olopierpa wrote:I must be doing something silly with this one (Problem 200(View Problem))

Can someone kindly check if the first few numbers satisfying the conditions are the following?

Your 4th number is not prime-proof. Add 400 and you get a prime.

### Re: Problem 200

Thanks for the help! (I have reduced the info posted, PM me if it's still not appropriate)

### Re: Problem 200

Done!

It was a silly one character mistake.

Now on to the problem thread, to see all the wonderful optimization opportunities I missed.

It was a silly one character mistake.

Now on to the problem thread, to see all the wonderful optimization opportunities I missed.

- PhilLeTaxi
**Posts:**20**Joined:**Wed Mar 05, 2014 12:54 pm**Location:**Paris, France

### Re: Problem 200

Hi,

Can someone tell me if the following squbes are correct ?

5th : 71952008

50th : 20074469192

100th : 102005604488

Can someone tell me if the following squbes are correct ?

5th : 71952008

50th : 20074469192

100th : 102005604488

- PhilLeTaxi
**Posts:**20**Joined:**Wed Mar 05, 2014 12:54 pm**Location:**Paris, France

### Re: Problem 200

OK, I solved the problem.

The 50th and the 100th mentionned above were not correct.

The 50th is : 20016803528

The 100th is : 72007089032

In fact, I was stopping the search too earlier and missed some smaller squbes.

The 50th and the 100th mentionned above were not correct.

The 50th is : 20016803528

The 100th is : 72007089032

In fact, I was stopping the search too earlier and missed some smaller squbes.

### Re: Problem 200

How many primes should I generate?

I generated more than 203 million primes (sieved from ~4.29 billion numbers) but I could find only 26 prime-proof squbes containing 200.

The last of these 26 are:

<values removed by moderator>

Could someone please confirm whether my results are correct?

I generated more than 203 million primes (sieved from ~4.29 billion numbers) but I could find only 26 prime-proof squbes containing 200.

The last of these 26 are:

<values removed by moderator>

Could someone please confirm whether my results are correct?

Last edited by RobertStanforth on Tue May 01, 2018 8:38 am, edited 1 time in total.

**Reason:***Redacted partial results*