Question: Proof. Consider any number n. Let n! be the factorial of n, and consider the number p = n! + 1. So p is

Proof. Consider any number n. Let n! be the factorial of n,

Proof. Consider any number n. Let n! be the factorial of n, and consider the number p = n! + 1. So p is larger than n, and it has a remainder of 1 when divided by any number up to n. So p is prime, and we have therefore found a prime number above n. So there are infinitely many prime numbers.

Step by Step Solution

★★★★★

3.42 Rating (142 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

This is a proof by contradiction of Euclids theorem which states that there are infinitely many ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

The surfaces = 3, = 5, = 100, = 130, z = 3, and z = 4.5 define a closed surface. Find (a) The enclosed volume; (b) the total area of the enclosing surface; (c) The total length of the twelve...

1. Show that any integer n can be written uniquely as n = nim, where m is squarefree, i.e. is not divisible by any square of a prime. [10 marks] 2. Let Pj be the jth prime for some je N. Let N; (x)...

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

1. Let p be a prime number which is neither 2 nor 3. Prove that either p = 1 mod 6 or p = -1 mod 6. 2. Prove that there are infinitely many primes p such that p = -1 mod 6. Hint: Suppose on the...

Using the Model of the Cultural Process , can you describe for me: 1. Exactly what cultural meanings do these smart speakers hold? 2. How did smart speakers gain their cultural meanings? Please be...

Problem 1. (10 points) Let p be a prime number. In class we proved that every non-zero element of Zp has a multiplicative inverse. Since 1.11 (mod p) it is obvious that 1-1 1 (mod p). In other words,...

Confirming Pages C H A P T E R 19 Analyzing Information and Writing Reports Chapter Outline Using Your Time Efficiently Analyzing Data and Information for Reports Identifying the Source of the Data...

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

Recall that N is the set of positive integers and Q is the set of rational numbers. NOTE: "Limit point\Sequences - Part 2 (Week 4) Infinite Limits Definition. A sequence (sn) is said to diverge to +...

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

"Johannesburg - Procurement Chief at Woolworths Yogan Naidu has a passion for innovation, equality and job creation in South Africa. After just eight months in his position as head of Non-Trade...

Speculate on the nature of the relationship between the credit and collections department and the sales department at Wachusett Window in the last two questions.

Which list best represents common member benefits offered by laboratory professional societies? Replacement of interviews with society badges Guaranteed lifetime employment at member hospitals...

Zedek Corporation had net cash flows from operating activities during the past year of $216,000. During the year, the company expended $462,000 for property, plant, and equipment; sold property,...

At the beginning of the fiscal year, Andy Company purchased for $2,060,000 a patent that applies to the manufacture of a unique tamper-proof lid for medicine bottles. Andy incurred legal costs of...

A partial list of Cottonwood Medical Centers costs is provided below a. Depreciation of X-ray equipment b. Salary of the nutritionist c. Cost of advertising hospital services on television d. Cost of...

A partial list of Foothills Medical Center's costs follows: a. Cost of patient meals b. Nurses' salaries c. Depreciation of X-ray equipment d. Utility costs of the hospital e. Salary of intensive...

What four methods are used to account for inventory? What are the financial implications of one method over another? How does the choice of inventory accounting method affect the order in which...

Sketch the region bounded by the given equations. Express the region's area asan iterated double integral and evaluate the integral.y=ex,y=0,x=0,x=ln12Choose the correct form of the...

In this exercise, we explore the concept o f marginal rates of substitution (and, in part B, its relation to utility functions) further. A: Suppose I own 3 bananas and 6 apples, and you own 5 bananas...

Suppose you have $400,000 to spend on a house and other goods (denominated in dollars). A. The price of 1 square foot of housing is $100 and you choose to purchase your optimally sized house at 2000...

In Chapter 22, we worked with models in which high and low cost customers compete for insurance. Consider the level x of health insurance that consumers might choose to buy, with higher levels of x...

A manager wishes to estimate a population mean using a 95% confidence interval estimate that has a margin of error of 44.0. If the population standard deviation is thought to be 680, what is the...

A public policy research group is conducting a study of health care plans and would like to estimate the average dollars contributed annually to health savings accounts by participating employees. A...

A decision maker is interested in estimating the mean of a population based on a random sample. She wants the confidence level to be 90% and the margin of error to be 0.30. She does not know what the...