8675309^2-1 just passed index of 3000
 

Been working on this one(75260986245480) for a little while on factordb, currently around 82 digits.

That is all.

Is there any special of this number?

867-5309 is a phone number used as a chorus of a famous American pop song from a generation or two ago.

That's a long one. If it terminates, it may break the record for longest known terminating sequence. We won't know until it terminates, if ever. It will have to have at least 12320 terms (the current record).

Been slowly pushing this along with gnfs, hopefully a down driver emerges soon.

Index:3327
Digits:124

[url]http://factordb.com/sequences.php?se=1&aq=8675309%5E2-1&action=last20&fr=0&to=100[/url]

[QUOTE=VBCurtis;391444]867-5309 is a phone number used as a chorus of a famous American pop song from a generation or two ago.[/QUOTE]


[url]http://youtu.be/eND16kC79pw[/url]

8675309 is also a prime

Index: 3358
Digits: 136

Still working on it but it is accelerating straight up now so this may be the end of the line. Was a fun ride though.

Other things about 8675309
 

[QUOTE=pdazzl;394011][URL]http://youtu.be/eND16kC79pw[/URL]

8675309 is also a prime[/QUOTE]Hello.

- 8,675,309 and 8,675,311 make a set of twin primes.

- According to [URL]http://primes.utm.edu/curios/page.php/8675309.html[/URL] , The hypotenuse of a (primitive) Pythagorean triple: 8675309^2 = 2460260^2 + 8319141^2.

About 5 years ago, I’ve found something else that I think is interesting about 8675309:
- Go to [URL]http://www.alpertron.com.ar/ECM.HTM[/URL]
- Uncheck Automatic switch to SIQS
- Check Verbose mode
- Check Use Cunningham tables on server
- In the blank for “Number of digits in a group,” set it to 999
- Click Change
- In the top blank type in [B]8675309^1000+1[/B] and press Enter
-[B] 8675309^1000+1[/B] is a composite with over 6000 digits and in about 20 seconds it will very quickly reveal a prime factor with over 1000 digits for some reason. I once emailed the creator of the applet about this being interesting and he said something about arithmetic or Aurifellian numbers causing it. I was amazed to find a prime factor with over 1000 digits from a composite number with over 6000 digits so quickly! :smile:

This is unbelievably hard to understand. [URL="http://factordb.com/index.php?query=%288675309%5E200%2B1%29%2F%288675309%5E40%2B1%29"]Not[/URL].

[QUOTE=VBCurtis;391444]867-5309 is a phone number used as a chorus of a famous American pop song from a generation [B]or two[/B] ago.[/QUOTE]

Yikes! You must be counting Mississippi generations there :smile:. The song ([I]Jenny/867-5309[/I] by Tommy Tutone) came out in my birth year, 1982. I have yet to meet any grandparents among peers of mine. Hells bells, most of us still live with our own parents, never mind taking out mortgages, being fruitful, and multiplying.

Although, I should add that (for better or worse) it is not impossible for such to be extant. My great-aunt Ruby was born in 1929 to a 14-year-old mother and a 29-year-old father. (This was in North Carolina; obviously both the statutory rape laws and Daddy's shotgun failed the young lady. The birth certificate lists a respectable 16 for Mom and 21 for Dad, ages that seem to have been commonly set as the minimum for the giving away of a daughter's hand by Southern families in the 19th and early 20th Centuries.) The two of them ended up being married and having several other children. Ruby would then go on to have her first child at the tender (or perhaps in this case, ripe old) age of 17, making Ruby's mother a 31-year-old grandmother and subsequently a great-grandmother by her early fifties. Sadly, I don't believe she made it to great-great-grandmother before her death at 71.

The son of the fellow that painted our house in Maine last year managed to get a girl pregnant when he was 15 and she was 13. Amazingly, they were still together three years later, doing their best to raise the child. Unfortunately, I think they bumped heads too much to attempt marriage. But they too could end up being thirty-something grandparents.

Consider:
Baby Boomers, born 1945-1964.
Gen X, 1965-1982ish
etc
A generation, as used for grouping people/events/styles, is 16-20 yrs. That song is over 30 years old, making it well more than a generation old, in fact very nearly two full generations old.

Nirvana is a generation ago.