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The reciprocal of five conventionally appears twice in the sum. The sum of the reciprocals of the Proth primes, of which there may be finitely many or infinitely many, is known to be finite, approximately 0.747392479. [2] The prime quadruplets are pairs of twin primes with only one odd number between them.
Prime (p)Period length Reciprocal (1/p) 2 0 0.5 3 † 1 0. 3 5 0 0.2 7 * 6 0. 142857 11 † 2 0. 09 13 6 0. 076923 17 * 16 0. 0588235294117647 19 * 18 0. 052631578947368421 23 * 22 0. 0434782608695652173913
For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution). Multiplying by a number is the same as dividing by its reciprocal and vice versa ...
Slices of approximately 1/8 of a pizza. A unit fraction is a positive fraction with one as its numerator, 1/ n.It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number.
(see the Basel problem), the above constant log 5 / 3 = 0.51082... can be improved to log π 2 / 6 = 0.4977...; in fact it turns out that ( ) = where M = 0.261497... is the Meissel–Mertens constant (somewhat analogous to the much more famous Euler–Mascheroni constant ).
The observations about −3 and 5 continue to hold: −7 is a residue modulo p if and only if p is a residue modulo 7, −11 is a residue modulo p if and only if p is a residue modulo 11, 13 is a residue (mod p) if and only if p is a residue modulo 13, etc. The more complicated-looking rules for the quadratic characters of 3 and −5, which ...
For example, America’s top source of the imported metals, Canada, sends $7 billion a year in steel and $9 billion in aluminum to the U.S. That’s just a fraction of the nearly $500 billion in ...
This is used in the special number field sieve to allow numbers of the form x 11 ± 1, x 13 ± 1, x 15 ± 1 and x 21 ± 1 to be factored taking advantage of the algebraic factors by using polynomials of degree 5, 6, 4 and 6 respectively – note that φ (Euler's totient function) of the exponents are 10, 12, 8 and 12.