Largest Known Prime Number Found

[mosaix]

Largest known prime number discovered in Missouri - BBC News

The largest known prime number has been discovered by a computer at a university in Missouri in the US.

The new prime is more than 22 million digits long, five million longer than the previous largest known prime

22 million digits!

 

[J Riff]

Shades of The Cube. How many Gigabytes of text is that I wonder.

 

[Ray McCarthy]

How many Gigabytes of text is that I wonder.

Encoded as ASCII, only 0.022G Bytes of Text. As Packed BCD it's 0.011G Bytes. Less as unsigned binary integer representation approximately 0.0086 G Byte, or 8.6 M byte. At most the text without commas, spaces or newlines would be 0.044G Bytes.

 

[J Riff]

That is peanuts. We can all have the biggest prime number backed up on a little memory card from our digicams?
And what the heck is packed BCD? Binary Code Derangement?

 

[Mirannan]

That is peanuts. We can all have the biggest prime number backed up on a little memory card from our digicams?
And what the heck is packed BCD? Binary Code Derangement?

Binary Coded Decimal, I believe.

 

[mosaix]

Binary Coded Decimal, I believe.

Correct!

 

[Ray McCarthy]

Yes, Packed Binary Coded Decimal is two decimal digits per computer byte. Here is why:
A byte is eight bits. value could be 0 to 255, i.e. 256 possibilities. Half a byte is a Nybble, or four bits, i.e. 0 to 15 or 16 possible values. Binary coded Decimal uses 0000 to 10001 (0 to 9), Packed BCD uses two "nybbles" per 8 bit byte.
Thus from earliest days of computers in 1950s the Packed BCD was popular. Modern CPUs may have special hardware to speed up usage, historically it saved half storage but had to be "unpacked" to binary integers for arithmetic.

A Word is machine size / CPU type dependant and can be:
10 bits (1024 values)
12 bits (4096) Some 8 bit CPUs actually use 12 bit or 14 bit "words" in Program Memory
14 bits (16384 values)
16 bits (65536)
32 bits (4294967296 values)
64 bits (1.844674407×10¹⁹ values)

Signed Integers use half as many values per word as the most significant bit is the sign.

Note that physical addressing maybe unrelated to "word" size. Thus addressing can be 10 bits to 20 bits on an 8 bit CPU, and on 32Bit or 64bit CPUs can be 40 bits to 48 bits. Virtual and/or MMU internal CPU addressing is often more than the physical addressing possible.

 

[Ray McCarthy]

We can all have the biggest prime number backed up on a little memory card from our digicams?

About 2000 copies of it on a little finger nail sized card.

 

[J Riff]

But how many pages in a book is 22 mil characters? A trilogy? T'isnt fair because each word is only one number, and would only be of interest to, to ..... nevermind. There may have been a SS idea there for a second, but it's gone.

 

[Ray McCarthy]

I'd guess about 20 fat volumes?

The word count is the number of words in a document or passage of text. Word counting may be needed when a text is required to stay within certain numbers of words. This may particularly be the case in academia, legal proceedings, journalism and advertising. Word count is commonly used by translators to determine the price for the translation job. Word counts may also be used to calculate measures of readability and to measure typing and reading speeds (usually in words per minute). When converting character counts to words, a measure of 5 or 6 characters to a word is generally used

A 100,000 words can be about 400 pages. It depends on font size, margins and page format. That is approximately 700,000 characters including spaces, so at one digit per character and no commas, then 22/0.7 x 400 = 12,570 pages, or maybe 15.5K if you add a comma every third digit. So 20 fat volumes is possible.

A 32G byte SD card can carry about 25,000 eBook format novels. However it's variable as some may have images and some compression is possible. The internal storage of a Kindle or Nook might store over 2,000 books.