Large integers refer to integer values that exceed the typical range supported by standard data types in programming languages. In many programming languages, built-in integer types have limitations on the size they can represent due to memory constraints.

"Powers of ten" is a mathematical concept that refers to the notation of expressing numbers as a base of ten raised to an exponent. In this notation, a number is written in the form \(10^n\), where \(n\) is an integer. This concept helps in understanding and representing very large or very small numbers more conveniently.

A Zeisel number is a specific type of number that arises in the context of number theory, particularly in the study of integer sequences. It is defined as the smallest positive integer \( n \) for which the sum of the digits of \( n \) in base \( b \) is equal to \( n \).

The number 100 is an integer that follows 99 and precedes 101. It is a significant number in various contexts: 1. **Mathematics**: - It is a composite number, meaning it has factors other than 1 and itself (factors include 1, 2, 4, 5, 10, 20, 25, 50, and 100).

The number 113 is a natural number that follows 112 and precedes 114. It is an interesting number in several mathematical contexts: 1. **Prime Number**: 113 is a prime number, meaning it is greater than 1 and has no positive divisors other than 1 and itself. 2. **Odd Number**: 113 is an odd number since it is not divisible by 2.

An untouchable number is a positive integer that cannot be expressed as the sum of the proper divisors (the divisors excluding the number itself) of any positive integer. In other words, there is no positive integer for which its proper divisors sum up to the untouchable number.

Weak ordering, in the context of preference relations and mathematics, refers to a situation in which items can be compared and ordered based on some criteria, but the order does not strictly define a comprehensive ranking. In weak ordering, two or more items can be considered equivalent in terms of preference, meaning that they can be equally preferred or ranked at the same level without establishing a definitive hierarchy among them.

A **weird number** is a specific type of integer in number theory that has a unique property regarding its divisors. Specifically, a weird number is defined as a positive integer that is abundant, meaning that the sum of its proper divisors (factors excluding the number itself) is greater than the number, but no subset of these divisors sums to the number itself.

The number 136 is an integer that comes after 135 and before 137. It is an even number and can be expressed in various ways, such as: - In Roman numerals, it is written as CXXXVI. - In binary, it is represented as 10001000. - In hexadecimal, it is represented as 88.

A Woodall number is a specific type of number in number theory that is defined as a number of the form \( n \cdot 2^n - 1 \), where \( n \) is a positive integer.

1,000,000 is the numeral representation of one million. It is a number that equals 10^6, which means it is 1 followed by six zeros (1,000,000). It is often used to denote large quantities, such as population figures, financial amounts, or statistical data.

The number 117 is an integer that comes after 116 and before 118. It is an odd number and can be expressed in various mathematical and contextual representations. Here are a few interesting facts about the number 117: 1. **Mathematical Properties**: - It is a composite number, meaning it has factors other than 1 and itself. The factors of 117 are 1, 3, 9, 13, 39, and 117.

The number 120 is an integer that comes after 119 and before 121. It has various mathematical properties: 1. **Even Number**: 120 is divisible by 2. 2. **Composite Number**: It is not a prime number; it can be divided by numbers other than 1 and itself.

The number 24 is a natural number that follows 23 and precedes 25. It is an even number and is often recognized for several mathematical and cultural significances. Mathematically, here are a few interesting facts about the number 24: 1. **Factorization**: 24 can be factored into prime numbers as \( 2^3 \times 3 \).

10,000 is a numerical value that can represent a quantity, an amount, or a measure in various contexts. It can refer to a count of items, a sum of money, a measurement in a specific unit, or be used in mathematical calculations. In the context of numbers, it is a four-digit number that follows 9,999 and precedes 10,001.

10,000,000 is a numerical figure that represents ten million. It's often used in finance, statistics, and various contexts to indicate a large quantity or amount. In numeric form, it can also be expressed as \( 10^7 \) in scientific notation.

100,000 is a numerical value that represents one hundred thousand. In terms of place value, it is made up of: - 1 (one hundred thousand) - 0 (ten thousand) - 0 (thousand) - 0 (hundred) - 0 (ten) - 0 (one) In various contexts, 100,000 can represent a quantity, such as people, dollars, or points.

The number 1001 is an integer that follows 1000 and precedes 1002. It is often recognized for its mathematical properties and cultural references. For instance: 1. **Mathematical Properties**: - It is an odd number. - It is a composite number, as it can be divided by numbers other than 1 and itself. Specifically, 1001 can be factored into prime numbers as \(7 \times 11 \times 13\).

The number 101 has several meanings and contexts depending on its usage: 1. **Mathematics**: In mathematics, 101 is a prime number that follows 100 and precedes 102. It is an odd number and does not have any divisors other than 1 and itself. 2. **Education**: In an academic context, "101" is often used to denote an introductory course in a particular subject.

The number 105 is a whole number that falls between 104 and 106. It is an odd number and can be expressed in several forms: 1. **Mathematical Properties:** - It is a composite number, meaning it has factors other than 1 and itself. The factors of 105 are 1, 3, 5, 7, 15, 21, 35, and 105.