31319

Properties

Appears in sequences

• Euclid-Mullin sequence (A000945) with initial value a(1)=5 instead of a(1)=2.at n=26A051308
• a(0)=1, a(n) = prime(n^3).at n=15A055875
• Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d=2,4 or 6) and forming d-pattern=[2, 6,6]; short d-string notation of pattern = [266].at n=12A078849
• Primes p such that the differences between the 5 consecutive primes starting with p are (2,6,6,4).at n=3A078950
• Smallest prime of the form concatenation of prime(n) with itself followed by a 9, or 0 if no such prime exists.at n=10A092995
• Primes of the form p*q + p + q, where p and q are two successive primes.at n=21A096342
• Numbers n such that 4*10^n + 2*R_n - 1 is prime, where R_n = 11...1 is the repunit (A002275) of length n.at n=9A102984
• (15^n)-th prime.at n=3A119776
• a(n) = prime(n)*prime(n+1) + prime(n) + prime(n+1).at n=39A126199
• Prime sequence overlaying the central digits of prime numbers. If possible, the value is greater than the previous one. Zero if no such embedding is possible.at n=31A133781
• Prime numbers p for which the quintic polynomial x^5 - x - 1 modulo p completely factors into linear polynomials.at n=27A135844
• Prime numbers p not of the form 10*k+1 for which the quintic polynomial x^5-x-1 modulus p is factorizable into five binomials.at n=21A135845
• Lesser of Twin prime numbers of the form : i^2+j^3, as sum of square and cube, if Greater Twin prime number also of the form : i^2+j^3, as sum of square and cube.at n=7A143799
• Primes of the form n^2 - 10.at n=14A201313
• Prime numbers generated by concatenating k, k, and 9.at n=6A210514
• Primes p with prime(p)^3 + 2*p^3 and p^3 + 2*prime(p)^3 both prime.at n=12A236574
• a(n) = prime(A003593(n)).at n=25A334276
• Lesser of twin primes (A001359) being both half-period primes (A097443).at n=30A347225
• Primes p such that if q is the next prime, (p+q)/6 is a triangular number.at n=41A356293
• Prime numbers p such that the product of their prime digits is equal to the product of their nonprime digits, where p has at least one prime digit.at n=22A369877