This number has 317 digits, all ones. It's prime. 317 is also prime! That's not a coincidence.

[mahatmakanejeeves]

This number has 317 digits, all ones. It's prime. 317 is also prime!

That's not a coincidence. A number whose digits are all 1 can only be prime if the number of digits is prime!

This works in any base, not just base ten. Can you see the quick proof?

(continued)

Link to tweet

[underpants]

1. Wow

[unblock]

2. cute! i think i have a concept for a proof:

if the number of digits is not prime, then the main number is divisible by a number of 1s equal in length of any of the number of digits' factors.

for example, if the main number is 15 ones in a row, this will be divisible by both 111 (three ones in a row) and 11111 (five ones in a row), as 3 * 5 = 15.

111111111111111 = 111 * 100100100100100

111111111111111 = 11111 * 100001000010000

[eppur_se_muova]

5. Exactly, and works in any base. Congrats !

Mersenne primes are repunits, base two, and only prime-exponent Mersennes can be prime. I believe the OP is referring to base ten, but many different bases have been explored.

[erronis]

3. You are all much smarter than me - I had to go looking for repunits

https://en.wikipedia.org/wiki/Repunit

Apparently 371 is the largest known prime, at this time.

Fascinating, and thanks for the neuron stimulation!

[erronis]

4. Corrected - looks like 270343 would be the longest 'probable' prime sequence of 1's

http://oeis.org/A004023

Don't think my laptop could handle the load to prove this though.

[lastlib]

6. I knew a guy who was a math professor at a nearby state university...

and serious computer geek. In the mid-90's, he wrote a program that would search for prime numbers. He started running it, and it runs to this day (even tho he died of cancer over a decade ago). It has identified a lot of very large prime numbers, including what I believe is the largest prime ever found: (2^30402457)-1. Vince was a really neat guy, and his death from brain cancer was really saddening to a lot of people.

[marble falls]

7. So how do we monetize this? Just asking for the guy in the next cubicle.

[Lucky Luciano]

8. Large primes are used in cryptography.

Do computer security etc.

[pennylane100]

9. I have a question that is not relevant to math but would love to know.

How would one pronounce the number in written language. Is it one hundred trillion, etc, etc, etc. I hope this question makes sense.

[mahatmakanejeeves]

10. That's plenty relevant. You want to know what prefix expresses the number's order of magnitude.

317 digits. Hmmm. There might not be a prefix for that.

Orders of Magnitude Prefixes for SI Units

It looks as if we stop at "exa," for ten to the 18th power.

Even a mole runs out at 10 to the 23rd power.

Sorry.

{Edited} Wait! Don't order yet! There's more!

How Big Is A Petabyte, Exabyte, Zettabyte, Or A Yottabyte?

Exabyte (1 000 000 000 000 000 000 Bytes)

• 5 Exabytes: All words ever spoken by human beings.
• From wikipedia:

• The world's technological capacity to store information grew from 2.6 (optimally compressed) exabytes in 1986 to 15.8 in 1993, over 54.5 in 2000, and to 295 (optimally compressed) exabytes in 2007. This is equivalent to less than one 730-MB CD-ROM per person in 1986 (539 MB per person), roughly 4 CD-ROM per person of 1993, 12 CD-ROM per person in the year 2000, and almost 61 CD-ROM per person in 2007. Piling up the imagined 404 billion CD-ROM from 2007 would create a stack from the earth to the moon and a quarter of this distance beyond (with 1.2 mm thickness per CD).
• The world’s technological capacity to receive information through one-way broadcast networks was 432 exabytes of (optimally compressed) information in 1986, 715 (optimally compressed) exabytes in 1993, 1,200 (optimally compressed) exabytes in 2000, and 1,900 in 2007.
• According to the CSIRO, in the next decade, astronomers expect to be processing 10 petabytes of data every hour from the Square Kilometre Array (SKA) telescope. The array is thus expected to generate approximately one exabyte every four days of operation. According to IBM, the new SKA telescope initiative will generate over an exabyte of data every day. IBM is designing hardware to process this information.

Some of those way-up-there prefixes sound invented to me.

[pennylane100]

12. Thank you for your answer

The information you gave was just mind boggling. I had no idea how complicated it is to measure date.

[mahatmakanejeeves]

13. De nada. And, from 2011: Scientists calculate total data stored to date: 295+ exabytes

Scientists calculate total data stored to date: 295+ exabytes
USC report calculates amount of stored data grew by 23% a year between 1986 and 2007

Lucas Mearian By Lucas Mearian
Senior Reporter, Computerworld | FEB 14, 2011 6:00 AM PT

Humankind has stored more than 295 billion gigabytes (or 295 exabytes) of data since 1986, according to a new report based on research by scientists at the University of Southern California.

The scientists also concluded that 2002 should be considered the beginning of the digital age because it was the first year digital storage capacity overtook total analog capacity worldwide.

The study, published this week in the Science Express journal, stated that "if a single star is a bit of information, there's a galaxy of information for every person in the world. But it's still less than 1% of the information stored in all the DNA molecules of a human being."
....

[robbob]

11. How many prime numbers are there? Guess...

***Spoiler alert (if you want to guess...)***


As hard to believe as it may seem, there are an infinite number of primes! The computer program described above will never stop finding new ones!

And the “proof”, elegant and simple?

If you take every prime number in the range of 1...x and multiply them together, then add “1”; voila! You have found a new prime number! This, of course, will not give you every prime number, you will skip over a bunch, but it will always give you a new prime number. So 2x3x5x7x11 etc etc +1 is a prime number.