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+ Every odd perfect number has at least 8 distinct prime factors. [Hagis]

+ 8 times the 8th prime has sum of digits equal to 8.

+ A prime quadruple is four consecutive primes, such that the first and last differ by 8.

+ - 1 + 23 * 45678 is prime. [Kulsha]

+ The smallest number which is the sum of two distinct odd primes.

+ The rightmost nonzero digit in 4013! (4013 is prime!) is 8. [Ottens]

+ The smallest cube which is the sum of a twin prime pair (3 + 5). [Trotter]

+ The smallest number which is both a sum of prime squares and a prime cube (8 = 22 + 22 = 23). [Kulsha]

+ The absolute difference between two odd prime squares is always a multiple of 8. [Capelle]

+ A Gaussian prime is a Gaussian integer p with exactly 8 divisors. [Smith]

+ Left-truncatable primes p of length n with the additional property that no prime with length n + 1 can have its leftmost digit removed to produce p are called Henry VIII primes.

+ 8 ones plus 8 is prime. [Opao]

+ 8 is the smallest sum of two factorials of distinct primes (2! + 3!). [Gevisier]

+ The largest number in which n is exactly twice pi(n). [Murthy]

+ Let p and q be odd primes. If p divides 2q - 1, then p = 1 (mod q) and p = + 1 (mod 8).

+ The largest composite number such that all its proper divisors + 1 are primes. [Murthy]

+ (108 - 8)/8 is prime. [Luhn]

+ (108+8 - 8)/8 is also prime. Thanks Mr. Luhn! [Poo Sung]

+ The first 'not possible' occurrence of summing k consecutive primes such that the total is prime happens when k = 8. [De Geest]

+ No Fibonacci number greater than 8 is ever of the form p-1 or p+1 where p is a prime number. [Honsberger]

+ The smallest composite Fibonacci number. [Gupta]

+ The 8th Fibonacci number plus and minus 8 is prime, i.e., F(8)-8 and F(8)+8 are primes. It is the smallest Fibonacci number to have this property. [Opao]

+ The product of the first k nonzero Fibonacci numbers + 1 is prime for k = 1, 2, 3, 4, 5, 6, 7, and 8.

+ Eight eights raised to the eighth power plus one is prime. I.e., 88888888^8 + 1 is prime. [Opao]

+ The first difference between consecutive primes of 8 is after 8*11+1. This is the last maximal gap of 4 consecutive even numbers. [Nicholson]

+ (8^8+88888)/8 is prime. Note that eight 8s are used. [Firoozbakht]

+ (pi(0)! + pi(1)! + ... + pi(k)!) is prime only for k = 1,2,..,8 (composite for k>8). [Firoozbakht]

+ 8 is the smallest composite number which can be represented as sum of two primes (i.e., 3 + 5) as well as sum of two composite numbers (i.e., 4 + 4). [Capelle]

+ Let R(n) = (10n - 1)/9 and Tn = the nth triangular number, then P(n) = TR(n) + 1 generates primes for n = 1 through 8. [Wesolowski]

+ The only composite digit that is not a semiprime. [Silva]

+ For n > 8, prime(n) > pi(n) + sigma(n), so 8 is the only number n such that prime(n) = pi(n) + sigma(n). [Firoozbakht]

+ The number of autobiographical primes is composite, but the number of autobiographical composites is prime. [Capelle]

+ The only known n such that the number of nonalternating knots with n crossings is prime. When n=8, there are 3 such knots. [Post]

+ The Riemann Hypothesis was number 8 on the list of problems that David Hilbert believed should set the course for the mathematical explorers of the twentieth century.

+ The only known cube that is the sum of the first n odd primes (3+5=8). [Bajpai]

+ The only integer that can be expressed as the average of first n consecutive right-truncatable primes, (n=5), i.e., (2+3+5+7+23)/5. [Loungrides]

(There are 18 curios for this number that have not yet been approved by an editor.)




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