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# 199

The smallest three-digit prime Lucas number.

Adding it to 210*n* provides the smallest 8, 9, and 10 primes in arithmetic progression.

(2^{199} + 1)/3 is the largest known Wagstaff prime which does not contain all of the individual digits.
[Luhn]

199 sets a record low of the Mertens function.

A permutable prime, meaning that 919 and 991 are primes as well. [Trotter]

The smallest number with an additive persistence of 3. [Gupta]

The smallest prime that can be concatenated with the next prime in any order giving two primes: 199211 and 211199. [Gallardo]

The Cape May Lighthouse in New Jersey has 199 steps in the tower's cast iron spiral staircase. [McCranie]

The smallest emirp that is also an invertible prime. [Punches]

In the Goldie Hawn/Chevy Chase movie *Foul Play*, Ferguson is kidnapped and held at building number 199.

The smallest prime that is the sum of the squares of four distinct primes. [Sladcik]

The smallest prime showing a repeated composite digit. [Silva]

Just average 101 & 297 to get this prime number. (Double Jeopardy! Round, February 1, 2010.)

The X-15 aircraft made 199 flights. [McCranie]

^{199}Hg (Mercury-199) is the heaviest stable atom
which has a prime atomic weight. [Hartley]

The half-life of Au-199 is approximately π days.

The sum of the digits of all three-digit palindromic primes. [Silva]

(199, 211, 223) is the first triple of primes of the form (p, p+12, p+24). Note that for p < 1000 is the only such triple. Note also that 199211 and 223211 are primes. [Loungrides]

In 1941, Molsen proved that for n equal to or greater than 199, the interval n < p less than or equal to (8/7)n always contains a prime of each of the forms 3x+1, 3x-1. [Post]

1000^199-999^199 is the only non titanic prime of the form p=1000^x-999^x. Note that the component 199 is equal to the smallest emirp of the form q=100^x-99^x. [Loungrides]

The first occurrence of a chain of six successive near-repdigit primes: 199, 211, 223, 227, 229, 233. [Beedassy]

The lesser of the smallest emirp pair (199, 991) each of whose members is the sum of a prime number of consecutive primes in a prime number of different ways: (199 = 61 + 67 + 71 = 31 + 37 + 41 + 43 + 47) ; (991 = 191 + 193 + 197 + 199 + 211 = 127 + 131 + 137 + 139 + 149 + 151 + 157). [Beedassy]

Largest known prime partial sum of Dedekind numbers. Equivalently partial sum of number of monotone Boolean functions of n variables, or partial sums of number of antichains of subsets of an n-set: 2 + 3 + 6 + 20 + 168 = 199 is prime. Curously, the first 5 such partial sums are prime (2, 5, 11, 31, 199), and then no more primes are known. [Post]

The smallest emirp formed from a double-digit number followed by the product of its digits. [Loungrides]

The smallest Lucas emirp. [Gudipati]

In visualizing the patterns generated in the "gaps of gaps" given by the prime numbers (e.g., below 199), a curious pattern emerges. This shows the gaps between the primes, followed by the absolute difference of those gaps, followed by the absolute difference of those gaps, etc., and on until all gaps are displayed in a (triangular) table of values. Done as a programming exercise, I was amazed to find patterns connecting common numbers in the table of gaps. Most interesting of these is the "dripping triangles" which reminds me of Wolfram diagrams. [Gene-Boggs]

The only prime that is the sum of three primes in a Honaker trios. [Chowdhury]

The first occurrence of a double-digit prime gap follows 199. [Lehmer]

The largest member in a set of twin primes generated by the formula n^2 + n(2n + 15) +/- 1 for n = 1 to 6. [Homewood]

The largest prime appearing on the Prime Numbers Activity chart by *Math is Fun*.

The smallest prime which is the sum of composite digits appearing in first primes up to itself. [Silva]

The smallest positive integer for which the sum of digits of its sum of digits is a two digit number. [Gaydos]

The smallest emirp p such that p and p^2 have the same sum of digits. [Gupta]