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19 Prime #1
Take nine pairs of numbers
(a,b) where a+b=19. Take the
sum a*b+19 for all of these
nine pairs; ALL of the sums are
primes. 19 is the LARGEST
prime that will do this.
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19 Prime #2
Pandigital palindromic primes
start as 19-digit numbers
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19 Prime #3
(11, 13, 17, 19) is the first prime
quadruple (p, q, r, s) such that
s divides pqr+1.
( $19 )
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19 Prime #4
There are exactly 19 primes
between
2^5 -1 and 2^7-1.
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19 Prime #5
The last 19 digits of
17^18 are prime.
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19 Prime #6
The only known prime of the
form p*prime(p)^p + 1, where p
is prime.
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19 Prime #7
19 is the smallest prime which
is the sum of three
discrete composites (4 + 6 + 9).
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19 Prime #8
19 is the only known prime of
the
form n^n - 8. The next prime in
this form (if it exists) will have
more than 34000 digits.
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19 Prime #9
Both numbers reversal (19! - 1)
and reversal ( 19! + 1) are
primes.
19 is the largest known prime
with this property.
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19 Prime #10
The largest prime that is
palindromic in Roman
numerals alphabetically is XIX
(19).
( $19 )
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19 Prime #11
The first prime p such that
p^2 is the reversal of a prime
(163).
( $19 )
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19 Prime #12
The following are primes: 19,
109, 1009, 10009. No other
digit can replace the 9 and
yield four primes.
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19 Prime #13
19 is the only known number
for which both (10^n-1)/9 and
(10^n+1)/11 are primes.
( $19 )
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19 Prime #14
19 is the only prime p less than
30 that does not divide 30,
where p + 30 is composite.
( $19 )
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19 Prime #15
19 is the smallest prime with a
digital root of 1.
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19 Prime #16
19 is the smallest prime of the
form 3p + 2q, where p and q
are twin primes.
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19 Prime #17
2^19 - 19 is prime.
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19 Prime #18
19 is the smallest prime whose
reversal is composite.
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19 Prime #19 (o)
(19 - 1) divides (19^19 - 1)
a prime number of times.
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