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Delano

Perfect numbers

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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

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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.

 

 

 

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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. 

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Here's the prime factor 131071.

@Troy

Can you figure out the other factors? 

If it is too hard I'll give you a smaller perfect number. 

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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

 

 

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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.

 

 

 

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131,071 is a Mersenne prime.

8,796,090,925,056 is a perfect number. 

So I have found something Mathematicians and computers have missed 

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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. 

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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!

 

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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. 

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@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? 

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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, 

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8 hours ago, Delano said:

Perhaps it is interesting to them

 

Yes, it is obviously interesting to them. My question is why? Why would anyone about the next astronomy large number no one can even say

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3 hours ago, Troy said:

Why would anyone about the next astronomy large number no one can even say

Different strokes 

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23 hours ago, Troy said:

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.

 

Yes, this is new to me! But I am very interested. 

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On 6/16/2019 at 12:24 AM, Troy said:

Is there is a practical application for discovering the next perfect prime? 

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

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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! 

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