Two primes which differ by 2 are known as twin primes. For example, 3 and 5...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Two primes which differ by 2 are known as twin primes. For example, 3 and 5 are twin primes, 11 and 13 are, and 461 and 463 are. One of the great unsolved problems in number theory is whether there are infinitely many twin primes. Are there any twin primes of the form 2n. = 1, 21, for n > 2? If so, give an example, and if not, prove there aren't any. Hint: From class, k, k + 1, k + 2 is a complete residue system modulo 3, for any choice of k. Two primes which differ by 2 are known as twin primes. For example, 3 and 5 are twin primes, 11 and 13 are, and 461 and 463 are. One of the great unsolved problems in number theory is whether there are infinitely many twin primes. Are there any twin primes of the form 2n. = 1, 21, for n > 2? If so, give an example, and if not, prove there aren't any. Hint: From class, k, k + 1, k + 2 is a complete residue system modulo 3, for any choice of k.
Expert Answer:
Related Book For
Introduction to Java Programming, Comprehensive Version
ISBN: 978-0133761313
10th Edition
Authors: Y. Daniel Liang
Posted Date:
Students also viewed these mathematics questions
-
is a legally recognized process for resolving disputes that involves the parties placing their cases before an unbiased third party
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
Q1. You have identified a market opportunity for home media players that would cater for older members of the population. Many older people have difficulty in understanding the operating principles...
-
Consider the following propositions: p: 2 is the smallest prime q: 6 is a perfect square Represent the proposition "2 is the smallest prime but 6 is not a perfect square" using logical connectives....
-
Why do eyeglasses, cameras lenses, and binoculars with antireflective coatings often look faintly purple?
-
Howell Corporation produces an executive jet for which it currently manufactures a fuel valve; the cost of the valve is indicated below: Cost per Unit Variable costs Direct material $900 Direct labor...
-
Let \(f(x)\) be defined for \(x \in[-L, L]\). Parseval's identity is given by \[\frac{1}{L} \int_{-L}^{L} f^{2}(x) d x=\frac{a_{0}^{2}}{2}+\sum_{n=1}^{\infty} a_{n}^{2}+b_{n}^{2}\] Assuming the the...
-
House of Organs, Inc., purchases organs from a well-known manufacturer and sells them at the retail level. The organs sell, on the average, for $2,500 each. The average cost of an organ from the...
-
Explain with THREE (3) reasons how can organizations improvethe effectiveness of their recruiters ?(10 marks) 2 answers
-
Univex is a calendar year, accrual basis retail business. Its financial statements provide the following information for the year: Revenues from sales of goods $ 783,200 Cost of goods sold (FIFO) ...
-
You have $63,000. You put 23% of your money in a stock with an expected return of 12%, $39,000 in a stock with an expected return of 13%, and the rest in a stock with an expected return of 21%. What...
-
As a hospital administrator, you hear some complaints and want to investigate whether the problem of stereotyping exists at your facility. How will you conduct the investigation? What will you do if...
-
a) b) Briefly describe the determination of bearing capacity based on the following methods: i) Standard Penetration Test ii) Analytical Methods approach (at least two methods that you have learnt)...
-
Prepare a bare total estimate for the given Masonry work using Standard Bricks. Joint thickness is in and brick size is 4 % x 24 x 9 3/8 inches. Include Scaffolding for bonus points! -30'- .8-.9 +3...
-
= Let {0,1} and consider the following context-free grammar: G = (V,E,R,S) where: V = {S,T} R is defined as: SOT T1 | e T 0SS1 and the following regular expression: (a) Prove that L(E) L(G) (b) Prove...
-
A 5 kg object is released, from rest, at a height of h = 3 Rmoon above the surface of the Moon, where Rmoon = 1740 km is the radius of the Moon. The mass of the Moon is 7.3 x 1022kg. (a) What is its...
-
The goose has a mass of 21.8 lb (pounds) and is flying at 10.4 miles/h (miles per hour). What is the kinetic energy of the goose in joules?
-
One study found that the elderly who do not have children dissave at about the same rate as the elderly who do have children. What might this finding imply about the reason the elderly do not dissave...
-
Write a program that prompts the user to read two integers and displays their sum. Your program should prompt the user to read the number again if the input is incorrect.
-
The area of a pentagon can be computed using the following formula: Write a method that returns the area of a pentagon using the following header:public static double?area(double?side)Write a main...
-
Listing 8.3 gives a program that finds two points in a two-dimensional space nearest to each other. Revise the program so that it finds two points in a three-dimensional space nearest to each other....
-
Some liabilities are reported at their maturity amount. In general, when should liabilities, prior to the maturity date, be reported at less than their maturity amount?
-
In evaluating a balance sheet, some creditors say the liability section is one of the most important sections. What are some reasons justifying this position?
-
Compute the present value of a \(\$ 10,000\), one-year note payable that specifies no interest, although \(10 \%\) would be a realistic rate. Is the present value less than, greater than, or equal to...
Study smarter with the SolutionInn App