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pr-Prime Numbers

Look at this number:

11732185257448480166176242876112284486042742946131111493953183550895075811 
11973086857454524059995754051178328588785835318415029838850875091778558864 
902895107205590716638457567080120811328335840498029896573618086708333433

What is so special about it? Well, it is a prime number. Moreover it is a prime number of a special form N º p (mod q), where N, p and q are all primes. Moreover it is a prime number, which is

N º 541 (mod 547)
N º 523 (mod 541)
N º 521 (mod 523)

N º 7 (mod 11)
N º 5 (mod 7)
N º 3 (mod 5)
N º 2 (mod 3)
N º 1 (mod 2)

See how handy it is: simply remember two primes - this one and 547 - and you can get a list of the first 100 prime numbers at once just like this whenever you want it :)

But speaking seriously, the practical implication of such prime numbers is questionable, the only reason I’m spending my time on this subject is because I found it curious.

NB: “Pr-prime” is not a standard mathematical or cryptographical term; “pr” here simply stands for “prime reminders”

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