Problem 050

persa · Post by **persa** » Tue Jul 29, 2008 8:11 am

I think that something's going wrong! The number 953 is prime but it isn't the longest sum of consecutive primes below one-thousand that adds to a prime. The number 281 has this property with 14 terms.
According to this, the prime, below one-million, which can be written as the sum of the most consecutive primes, is 958577 with 536 terms, but my answer is wrong. I wonder why?

harryh · Post by **harryh** » Tue Jul 29, 2008 8:24 am

The problem states that 953 is a sum of 21 consecutive primes (actually : 7+11+13+...+83+89).
Isn't that a longer sum than the 14 terms adding up to 281 ?

persa · Post by **persa** » Tue Jul 29, 2008 9:20 am

ok thanks!
I thouhgt that the sum should begin always from 2 (the first prime)

iamhigh · Post by **iamhigh** » Tue Sep 29, 2009 10:34 am

These consecutive numbers start from 2 or any prime number?

harryh · Post by **harryh** » Tue Sep 29, 2009 11:32 am

Well, as you can see there was already a topic for this problem (I have just merged the two topics). So:
(a) There was no need to start a new topic.
(b) The answer to your question was there already

iamhigh · Post by **iamhigh** » Mon Oct 05, 2009 11:19 am

Thanks harryh - I can swear I searched for "Problem 050" but nothing showed up on the search results - Do they get archived after a period of neglect?

daniel.is.fischer · Post by **daniel.is.fischer** » Mon Oct 05, 2009 1:25 pm

No, but the search term "Problem xxx" is too generic to produce results.

Go to the bottom of the forum page, there you have the opportunity to change by which criteria the topics are sorted. Sort by subject, and it's easy to find (if it's there already).

srmackey · Post by **srmackey** » Wed Nov 04, 2009 2:04 pm

The problem states:

"The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953."

II always come up with something different. I get 961 as a sum of 23 primes.

961 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89

Can anyone verify if my answer is incorrect? I have solved the problem, but I'm curious about this discrepancy.

genious999 · Post by **genious999** » Wed Nov 04, 2009 2:21 pm

srmackey wrote:The problem states:

"The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953."

II always come up with something different. I get 961 as a sum of 23 primes.

961 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89

Can anyone verify if my answer is incorrect? I have solved the problem, but I'm curious about this discrepancy.

961=31*31, so that sum is not a prime.

srmackey · Post by **srmackey** » Thu Nov 05, 2009 1:10 am

genious999 wrote:961=31*31, so that sum is not a prime.

Ah... good call. There must be something wrong with my sieve algorithm. Thanks for the feedback!

abranches · Post by **abranches** » Sat Nov 20, 2010 2:53 pm

Why the largest below 1000 is
953 = 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89
and not
983 = 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97

Both are primes and the sum of primes in sequence.
So the largest should be 983. What I'm doing wrong here?

Ok I got it... is the largest in number of terms.

JMW1994 · Post by **JMW1994** » Sat Apr 16, 2011 6:16 am

abranches wrote:Why the largest below 1000 is
953 = 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89
and not
983 = 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97

Both are primes and the sum of primes in sequence.
So the largest should be 983. What I'm doing wrong here?

Ok I got it... is the largest in number of terms.

Why did you skip 2,3, and 5? At 21 numbers, I get 712, but 281 was the largest so I'm wrong somewhere.

thundre · Post by **thundre** » Sun Apr 17, 2011 12:49 pm

JMW1994 wrote:Why did you skip 2,3, and 5? At 21 numbers, I get 712, but 281 was the largest so I'm wrong somewhere.

712 is not prime.

JMW1994 · Post by **JMW1994** » Sun Apr 17, 2011 11:19 pm

thundre wrote:
JMW1994 wrote:Why did you skip 2,3, and 5? At 21 numbers, I get 712, but 281 was the largest so I'm wrong somewhere.
712 is not prime.

Well, I knew that. The problem states:

The prime 41, can be written as the sum of six consecutive primes:

41 = 2 + 3 + 5 + 7 + 11 + 13
This is the longest sum of consecutive primes that adds to a prime below one-hundred.

The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953.

Which prime, below one-million, can be written as the sum of the most consecutive primes?

When I tried to solve the largest one-thousand consecutive prime and I had 21 prime terms,including 2, 3, and 5, I got the number 712 which is obviously a composite number. I got 281 as the largest which wasn't correct. Besides, I never got and answer from my last question. The question was: Why did you skip 2,3, and 5?

jaap · Post by **jaap** » Sun Apr 17, 2011 11:35 pm

JMW1994 wrote:The question was: Why did you skip 2,3, and 5?

Why not? The question states only that the sequence of primes is consecutive, not that it must start at 2.

JMW1994 · Post by **JMW1994** » Fri Apr 22, 2011 11:28 pm

My next question is why isn't 2, 3, or 5 consecutive?

TripleM · Post by **TripleM** » Sat Apr 23, 2011 12:23 am

Your questions aren't really making much sense.. 2, 3, and 5 are consecutive primes; they're even shown in the example in the problem as being consecutive primes. Nobody has said that they aren't.

apdwyer51 · Post by **apdwyer51** » Sat Dec 31, 2011 6:21 pm

I have a question about the directions for this problem. When you click on the problem it gives the following examples:

it adds the first 6 primes and gets 41 then says that this: This is the longest sum of consecutive primes that adds to a prime below one-hundred. I get this.

Then it says:

The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953.

But when I add the first 21 prime numbers together, I get 712, not 953. When I add the first 24 primes together, I get 963, completely skipping 953. This makes me think that I don't quite understand what the problem is asking.

Can someone explain how the first 21 terms gives 953?

Thanks.

wrongrook · Post by **wrongrook** » Sat Dec 31, 2011 7:15 pm

The sum does not have to start with 2.

e.g. 7+11+13 = 31 would be another example.

Eternalcode · Post by **Eternalcode** » Sat Dec 31, 2011 11:08 pm

When the problem says

"The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953."

That does not mean
from 2 to the 21st prime number below one-thousand.

Whenn you add X amonunt of consecutive primes below that upperbound, it should result in being the longest chain within on-thousand.

Good luck.

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