![](/files/happy5.png)
prime
Sum of prime and semiprime conjecture ★★
Author(s): Geoffrey Marnell
Conjecture Every even number greater than
can be represented as the sum of an odd prime number and an odd semiprime .
![$ 10 $](/files/tex/f9664c0e5fcffbbe88ed551c02b9275233d8f6b4.png)
Polignac's Conjecture ★★★
Author(s): de Polignac
Conjecture Polignac's Conjecture: For any positive even number n, there are infinitely many prime gaps of size n. In other words: There are infinitely many cases of two consecutive prime numbers with difference n.
In particular, this implies:
Conjecture Twin Prime Conjecture: There are an infinite number of twin primes.
Are there an infinite number of lucky primes? ★
Author(s): Lazarus: Gardiner: Metropolis; Ulam
Conjecture If every second positive integer except 2 is remaining, then every third remaining integer except 3, then every fourth remaining integer etc. , an infinite number of the remaining integers are prime.
Twin prime conjecture ★★★★
Author(s):
Conjecture There exist infinitely many positive integers
so that both
and
are prime.
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ n+2 $](/files/tex/b244e658e84df66f052dfb93b9ab0b2dd5e5af26.png)
Keywords: prime; twin prime
Wall-Sun-Sun primes and Fibonacci divisibility ★★
Author(s):
Conjecture For any prime
, there exists a Fibonacci number divisible by
exactly once.
![$ p $](/files/tex/928cd9d544fdea62f88a627aaee28c416c4366c0.png)
![$ p $](/files/tex/928cd9d544fdea62f88a627aaee28c416c4366c0.png)
Equivalently:
Conjecture For any prime
,
does not divide
where
is the Legendre symbol.
![$ p>5 $](/files/tex/a9737aaa01b2918b7e8ab9f12ab0a7c463381427.png)
![$ p^2 $](/files/tex/8f6ab14c3cc11c005c9b97778062620c197ff66d.png)
![$ F_{p-\left(\frac p5\right)} $](/files/tex/e1a04059df8fc3e49db781f306092d0d564732e3.png)
![$ \left(\frac mn\right) $](/files/tex/d8d0b3deced8bb07e56b3da3337f2d8c7db060a1.png)
Goldbach conjecture ★★★★
Author(s): Goldbach
Conjecture Every even integer greater than 2 is the sum of two primes.
Keywords: additive basis; prime
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