...is this really a surprise? I'm sure if you start including more digits you'll get to another prime eventually too. That's the fun part of having infinitely many digits to play with.
@standupmaths
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This is supported by the prime number theorem: the probability that a number more or less 10^k is prime is about 1/k, hence the probability that some first k digits of random number is prime is one.
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There's a big prime beginning at every decimal. If you type random numbers, the string of digits will sooner or later hit on a prime. Instead of random numbers, you can even encode the text of your choice in the prime number! https://en.m.wikipedia.org/wiki/Illegal_prime …
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For instance, pi has many primes from the first digit: 3, 31, 314159, 31415926535897932384626433832795028841 and one prime consisting of the first 16208 digits. (OEIS A005042)
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e-Primes are primes appearing in the initial digits of the decimal expansion of e. The largest known e-prime has 155025 digits http://oeis.org/A007512 . Like π-primes http://oeis.org/A005042 or φ-primes http://oeis.org/A064117 or http://mathworld.wolfram.com/IntegerSequencePrimes.html …pic.twitter.com/9Y4Tcsdx55
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This gives me an idea for the OEIS : a(n)=k iff the first n-digit prime in the decimals of e (ignoring the integer part 2) starts at rank k. e=2.7182818284590452353... a(1)=1 because 7 is prime. a(2)=1 bc 71 is prime, a(3)=4 bc 281 is prime, a(4)=14 bc 4523 is prime, ...
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I think "quickly" is a bit of a stretch to be honest. Might just be me...
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You quickly find the prime number 7
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My new password
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