1.3 Factors and Multiples
... The Lowest Common Multiple (LCM) of two or more whole numbers is the smallest multiple that is common to those numbers. The LCM can be determined from one of the following methods: Method 1: First, select the largest number and check to see if it is divisible by all the other numbers. If it divides ...
... The Lowest Common Multiple (LCM) of two or more whole numbers is the smallest multiple that is common to those numbers. The LCM can be determined from one of the following methods: Method 1: First, select the largest number and check to see if it is divisible by all the other numbers. If it divides ...
Deterministic elliptic curve primality provingfor a special sequence of
... similar numbers of a special form, the integers Jk are not amenable to any of the classical “N 1” or “N C 1” type primality tests (or combined tests) that are typically used to find very large primes (indeed, the 500 largest primes currently listed in [7] all have the shape ab n ˙ 1 for some small i ...
... similar numbers of a special form, the integers Jk are not amenable to any of the classical “N 1” or “N C 1” type primality tests (or combined tests) that are typically used to find very large primes (indeed, the 500 largest primes currently listed in [7] all have the shape ab n ˙ 1 for some small i ...
Exponents and Square Numbers
... A perfect square or a square number is the product of a number and itself. A square number can be represented with the exponent 2. ...
... A perfect square or a square number is the product of a number and itself. A square number can be represented with the exponent 2. ...
Least Common Multiple
... In the Real World Ferry Boats Two ferry boats leave a loading platform at the same time. One of the ferry boats returns to the loading platform every 25 minutes. The other returns every 30 minutes. In the next 300 minutes, when will they return at the same time? You can use multiples to answer the q ...
... In the Real World Ferry Boats Two ferry boats leave a loading platform at the same time. One of the ferry boats returns to the loading platform every 25 minutes. The other returns every 30 minutes. In the next 300 minutes, when will they return at the same time? You can use multiples to answer the q ...
Grade 6 Math Circles Divisibility Introduction Divisibility Tricks
... 2. The number 2 has two divisors, 1 and 2. The number 4 has three divisors, 1, 2, and 4. What is the smallest number with six divisors? 3. Mr. Lawrence wants to split his Grade 6 math class of 36 students into groups for an upcoming assignment. List all the possibilities of groups, each with the sam ...
... 2. The number 2 has two divisors, 1 and 2. The number 4 has three divisors, 1, 2, and 4. What is the smallest number with six divisors? 3. Mr. Lawrence wants to split his Grade 6 math class of 36 students into groups for an upcoming assignment. List all the possibilities of groups, each with the sam ...
Prime number theorem
In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. The theorem was proved independently by Jacques Hadamard and Charles Jean de la Vallée-Poussin in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function).The first such distribution found is π(N) ~ N / log(N), where π(N) is the prime-counting function and log(N) is the natural logarithm of N. This means that for large enough N, the probability that a random integer not greater than N is prime is very close to 1 / log(N). Consequently, a random integer with at most 2n digits (for large enough n) is about half as likely to be prime as a random integer with at most n digits. For example, among the positive integers of at most 1000 digits, about one in 2300 is prime (log(101000) ≈ 2302.6), whereas among positive integers of at most 2000 digits, about one in 4600 is prime (log(102000) ≈ 4605.2). In other words, the average gap between consecutive prime numbers among the first N integers is roughly log(N).