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> so I didn't know this, but got curious about how many known prime there are This isn't the exact question you're asking, but we actually know the distributio
by chimeracoder 9y ago
> so I didn't know this, but got curious about how many known prime there are
This isn't the exact question you're asking, but we actually know the distribution of prime numbers, which allows us to calculate the (approximate) number of primes that are less than or equal to an arbitrary value.
Since the largest prime discovered is 2^(277,232,917-1), that means that the number of primes less than or equal to that number is approximately equal to 2^(277,232,917-1)/ln(2^(277,232,917-1)).
That's approximately equal to:
2^(277,232,917-1)/ln(2^(277,232,917)), which is in turn equal to 2^(277,232,917-1)/(277,232,917 * ln(2)).
That's a number that's too big to plug into your standard everyday calculator, but that tells you the number of primes you could "discover" and still not break the (new) record.
- qmalzp 9y agoNit: the largest prime discovered is 2^(277,232,917)-1 not 2^(277,232,917-1)
- Franciscouzo 9y agoIf you read the article, it's actually: (2^77,232,917)-1
- TheRealPomax 9y agoNot sure if this was a serious comment, but if it was: due to operator precedence in mathematics, the expressions (2^77,232,917)-1, 2^(77,232,917)-1, and 2^77,232,917-1 are identically evaluated, with the parentheses only used to aid the human eye. This in contrast to 2^(77,232,917-1), which is 2^77,232,916 and is a very different number indeed.
- deleted 9y ago[deleted]
- kodablah 9y agoThe parens are a red herring. GP is commenting on the previous poster using 277 instead of 77 (i.e. typo).
- chrismorgan 9y agoVery well then; let us rather write them with proper superscripts (and I’ll use THIN SPACE as a thousands and prettiness separator too because I can): 2 ⁷⁷ ²³² ⁹¹⁷ − 1 not 2 ⁷⁷ ²³² ⁹¹⁷ ⁻ ¹ There, no more ambiguity. (Now I’m waiting for someone to jump on me to correct anything subtle.) [Ah, I see, the parentheses were indeed a red herring. Ah well; let the superscripts remain.]