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This is a question without much mathematical value, but since I don't immediately see an answer on Google I thought I'd ask anyway ... I'm looking for some largeish (> 10,000) easy-to-remember primes, like palindromes (313), numbers with decreasing digits 54321 (not a prime), etc. The primary purpose is for computer programs, where they are useful for hashing and the like.

What's your favorite, if you know any?

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closed as too broad by Najib Idrissi, voldemort, user98602, Shobhit, user147263 Jan 27 '15 at 18:19

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    $\begingroup$ The smallest prime greater than $10000$ is $10007$. $\endgroup$ – Git Gud Aug 19 '13 at 3:07
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    $\begingroup$ Nineteen $1$'s = $1111111111111111111$ is a prime. $\endgroup$ – Tito Piezas III Aug 19 '13 at 3:12
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    $\begingroup$ Sorry, what makes 65537 easy to remember? @Tito: love it, thanks! $\endgroup$ – gatoatigrado Aug 20 '13 at 2:46
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    $\begingroup$ The prime $2^{16}+1=65537$ is the biggest Fermat prime known so far. My example is called a repunit prime (only nine are known yet). P.S. I remember some of my Spanish, and I think "gato" means "cat". :) $\endgroup$ – Tito Piezas III Aug 20 '13 at 4:33
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Wikipedia's list of prime numbers includes "palindromic primes"

2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741

and "palindromic wing primes"

101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 11311, 11411, 33533, 77377, 77477, 77977, 1114111, 1117111, 3331333, 3337333, 7772777, 7774777, 7778777, 111181111, 111191111, 777767777, 77777677777, 99999199999.

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My personal favorite prime number is Belphegor's prime: $$1\underbrace{0000000000000}_{13}666\underbrace{0000000000000}_{13}1.$$ In addition to being palindromic, it has $31$ digits which is of course $13$ backwards.

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  • $\begingroup$ It appears that Is $1000000000000077700000000000001$ is prime also ? $\endgroup$ – Antonio Hernandez Maquivar Jun 10 at 17:44
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$$n^2 + n + 41$$

You can even change it to:

$$n^2 - n + 41$$

This gives primes for $n = 1$ to $n = 40$ (the first one has one less prime over the range for $n=40$).

There are variations that give 80 primes, but that formula has a 41 for 40 in a row, so easy to recall.

See many others at: http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html

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    $\begingroup$ You're on a roll!! +1 $\endgroup$ – Namaste Aug 19 '13 at 11:52
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Mersenne primes are pretty easy to remember... e.g. just remembering that 7 generates a double Mersenne gives you the 38-digit prime $2^{2^7-1}-1$. For smaller (but still "largeish") examples, $2^{17}-1$ and $2^{19}-1$ give 6-digit primes.

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31, 331, 3331, 33331, 333331, 3333331, 33333331 (7 threes). The next one is divisible by 17.

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$\qquad\quad$ I'm looking for some largeish (>10,000) easy-to-remember primes.

$$1~234~567~891.$$

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