Jump to content

Perfect numbers


Recommended Posts

A couple of them? Get out of here!

 

The 1st perfect number is 6. The 15th is shown below. There are maybe 50 or so known perfect numbers. If you found one smaller than the number below, that was not previously know, that is indeed a discovery!

 

What are you gonna do?

541,625,262,843,658,474,126,544,653,743,913,106,140,856,490,539,031,695,784,603,920,818,387,206,994,158,534,859,198,999,921,056,719,921,919,057,390,080,263,646,159,280,013,827,60543974626278890305730344550582702839513947520776904492443149486172943511312628083790493046274068171796046586734872099257219056946554529962991982343103109262424446354778963544148139171981644160558678809214788667732139875666162471455172696430221755428178425481731961195165985555357393778892340514622232450671597919375737282086087821432205222758453755289747625617939517662442631448031344693508520365758479824753602117288040378304860287362125931378999490033667394150374722496698402824080604210869007767039525923,189,466,627,361,521,277,560,353,576,470,795,225,017,385,830,517,102,860,302,123,489,664,785,136,394,992,890,497,329,214,510,750,597,991,145,622,151,989,934,576,498,429,128
Link to comment
Share on other sites

Hold up let me look something up, cause it can't be that simple....  from Wikipedia:

 

Rank p Perfect number Digits Year Discoverer
1 2 6 1 4th century B.C.[5] Euclid
2 3 28 2 4th century B.C. Euclid
3 5 496 3 4th century B.C. Euclid
4 7 8128 4 4th century B.C. Euclid
5 13 33550336 8 1456 First seen in a medieval manuscript, Munich, Bayerische Staatsbibliothek, CLM 14908, fol. 33[6]
6 17 8589869056 10 1588 Cataldi[1]
7 19 137438691328 12 1588 Cataldi[1]
8 31 2305843008139952128 19 1772 Euler

 

1+2+3=6

1+2+4+7+14=28

 

I wouldn't even want to calculate the next perfect number, 496, without a computer. The last perfect number was discovered in December of last year and it is an astronomically large number.

 

So if you show me a number below 9 million that you claim is a perfect number, I would have no way of verifying it, because I'd need to write a program to do it.  You would also need to provide the divisors that you used to prove it is correct.  Again, I sure someone else would have found them already -- especially if they are as small as you mentioned.

 

They have computers working on finding additional ones as we speak. This site says that all primes up to exponent 83 million have been verified: https://www.mersenne.org/report_milestones/ it also provides a countdown to verifying the ranges of numbers that are not perfect and that range is already absurdly large.

 

 

 

Link to comment
Share on other sites

It is not that easy. 

I will send you the factors in a day or so. 

Do you work with any mathematicians? 

 

I have also figured out a heuristic that may find all of the perfect numbers. 

Can you guess how many factors there are? 

 

 

I like patterns and numbers 

I will send you a spread sheet. 

Link to comment
Share on other sites

13 hours ago, Troy said:

A couple of them? Get out of here!

 

The 1st perfect number is 6. The 15th is shown below. There are maybe 50 or so known perfect numbers. If you found one smaller than the number below, that was not previously know, that is indeed a discovery!

 

What are you gonna do?

 

8 hours ago, Troy said:

Hold up let me look something up, cause it can't be that simple....  from Wikipedia

 

8 hours ago, Troy said:

wouldn't even want to calculate the next perfect number, 496, without a computer. The last perfect number was discovered in December of last year and it is an astronomically large number.

 

8 hours ago, Troy said:

wouldn't even want to calculate the next perfect number, 496, without a computer. The last perfect number was discovered in December of last year and it is an astronomically large number.

 

8 hours ago, Troy said:

 

So if you show me a number below 9 million that you claim is a perfect number, I would have no way of verifying it, because I'd need to write a program to do it.  You would also need to provide the divisors that you used to prove it is correct.  Again, I sure someone else would have found them already -- especially if they are as small as you mentioned.

 

They have computers working on finding additional ones as we speak. This site says that all primes up to exponent 83 million have been

I figured it out with pen paper and a calculator 

 

131,071 it appears that in have also found Merseme prones that computers haven't found 

@Cynique

@Mel Hopkins

@Chevdove

 

 

Link to comment
Share on other sites

No I don't know any mathematicians, but I can read.

 

Also, you are confusing me. You know prefect number ≠ prime number right?

 

What is this number 131,071?

 

I don't think there are any odd perfect numbers.

 

 

 

Link to comment
Share on other sites

Del the perfect number, 8,589,869,056, was discovered in the 16th century. It is on the list above I shared from wikipedia.

 

However, I'm impressed that you were able to derive it in your own. I'd encourage you to look into the work that has already heen done on the subject. 

Link to comment
Share on other sites

On 6/11/2019 at 7:01 PM, Delano said:

 

131,071 it appears that in have also found Merseme prones that computers haven't found 

 

This is all very fascinating to me and also 'way over my head'!--for now.

But I have been following this thread and planning to ask some questions to some smart people to help be better understand!

 

Link to comment
Share on other sites

I was wrong but Troy is more of the go to person for science and mathematics . 

Thanks Troy I found it because I happen to see a pattern in the first three. Which doesn't always work it gives false positives but it doesn't miss any of the numbers. 

Link to comment
Share on other sites

@Delano is being modest he probably knows more than me. I'd forgotten what a perfect number was until I looked it up. I was only sbke to coreect him because I'd just did a little research.

 

It also stuck me peole have computer actively looking for the next perfect number. It stuck me because I can't figure out the motivation to do it. Is there is a practical application for discovering the next perfect prime? 

Link to comment
Share on other sites

Perhaps it is interesting to them. 

EmirpsEdit

Primes that become a different prime when their decimal digits are reversed. The name "emirp" is obtained by reversing the word "prime".

13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 

Link to comment
Share on other sites

On 6/16/2019 at 6:53 PM, Troy said:

do you really care when and what the next perfect number is? If so why?

 

@Troy I am definitely interested and partly because I never really knew about this concept of 'a perfect number'. So it is intriguing because I do see the history of it now, But, I am trying to figure out now, what really is the importance of this subject and, if,  or how it is it used in relation to other concepts.

On 6/17/2019 at 5:09 AM, Delano said:

If there are patterns in primes. It changes encryption. and perhaps mathematics. 

 

Now, that is an amazing thought! 

  • Like 1
Link to comment
Share on other sites

The challenge with numbers is if applied wrongly can destroy us - 

since the only numbers I experiment with is in cooking - I'll leave it to the professionals and enthusiasts.  Speaking of which, my oldest daughter's sister is at Harvard right now because she's some kind of math wiz... she's only 15 - I admire her - she probably knows about perfect numbers and their uses :D

  • Like 2
Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
×
×
  • Create New...