44497

Properties

Appears in sequences

• Mersenne exponents: primes p such that 2^p - 1 is prime. Then 2^p - 1 is called a Mersenne prime.at n=26A000043
• Degrees of primitive irreducible trinomials: n such that 2^n - 1 is a Mersenne prime and x^n + x^k + 1 is a primitive irreducible polynomial over GF(2) for some k with 0 < k < n.at n=17A001153
• a(0) = 13; for n > 0, a(n) is the greatest prime factor of PreviousPrime(a(n-1))*a(n-1)-1 where PreviousPrime(prime(k))=prime(k-1).at n=9A031442
• Bisection of A000043.at n=13A099982
• Mersenne prime indices that are not Gaussian primes.at n=16A112634
• Smallest prime of the form: one or more 4's followed by prime(n) (or 0 if no such prime exists).at n=24A114786
• Primes p such that 2^p-1 is prime and congruent to 31 mod 5!.at n=15A145040
• Primes p (A000043) such that 2^p-1 is prime (A000668) and congruent to 271 mod 6!.at n=5A145044
• Base-2 logarithm of A136007(n)+1.at n=18A152961
• Isolated primes p such that 2^p-1 is also a prime number.at n=14A161676
• Primes containing the string 444.at n=10A166582
• Primes p such that 2*p-1 and 2^p-1 are both primes.at n=8A172461
• Odd Mersenne exponents.at n=25A174265
• Numbers k such that exactly one of 2^k - 1 and 2^k + 1 is a prime.at n=30A174269
• There appear to be at least n primes in the range (x-sqrt(x), x] for all x >= a(n).at n=12A189026
• Integers m such that m divides (2^m-2)^2 and (m-2)^((k-1)*(1+k*(m-1))) == 1 (mod k), where k = 2^m - 1.at n=27A190213
• Primes that are the sum of squares of three positive Fibonacci numbers.at n=36A191375
• Prime numbers n such that 2^n-1 is prime and can be written in the form a^2+7*b^2.at n=14A216518
• Odious Mersenne exponents.at n=14A237499
• Primes p such that 10p + 1, 100p + 1 and 1000p + 1 are also primes.at n=38A243962