# Is number 1 a prime number?



## Crystal (Aug 8, 2017)

I think number 1 is a prime number but many books say it isn't a prime number.


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## Art Rock (Nov 28, 2009)

The status of 1 as explained here:

In the mid-18th century Christian Goldbach listed 1 as the first prime in his famous correspondence with Leonhard Euler; however, Euler himself did not consider 1 to be a prime number. [6] In the 19th century many mathematicians still considered the number 1 to be a prime. For example, Derrick Norman Lehmer's list of primes up to 10,006,721, reprinted as late as 1956,[7] started with 1 as its first prime.[8] Henri Lebesgue is said to be the last professional mathematician to call 1 prime.[9] By the early 20th century, mathematicians began to arrive at the consensus that 1 is not a prime number, but rather forms its own special category as a "unit".[5]

A large body of mathematical work would still be valid when calling 1 a prime, but Euclid's fundamental theorem of arithmetic (mentioned above) would not hold as stated. For example, the number 15 can be factored as 3 · 5 and 1 · 3 · 5; if 1 were admitted as a prime, these two presentations would be considered different factorizations of 15 into prime numbers, so the statement of that theorem would have to be modified. Similarly, the sieve of Eratosthenes would not work correctly if 1 were considered a prime: a modified version of the sieve that considers 1 as prime would eliminate all multiples of 1 (that is, all other numbers) and produce as output only the single number 1. Furthermore, the prime numbers have several properties that the number 1 lacks, such as the relationship of the number to its corresponding value of Euler's totient function or the sum of divisors function.[10]


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## ST4 (Oct 27, 2016)

Ask these guys:


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## EddieRUKiddingVarese (Jan 8, 2013)

Lets see who will be the first to vote on this one- will they be the prime voter?


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## ArtMusic (Jan 5, 2013)

1 is an odd number. That's a fact.


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## SixFootScowl (Oct 17, 2011)

Whether or not 1 is prime depends on the definition of what is a prime number.


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## Tristan (Jan 5, 2013)

As a number theory hobbyist, 1 being prime does not fit into my understanding of prime numbers. So no, I do not consider it prime, and consider 2 to be the first prime number. So yes, it does depend on your definition of prime; to me it means a number that has exactly 2 divisors: 1 and the number itself. Thus 1 itself is excluded.


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## JeffD (May 8, 2017)

No, one is not a prime number. By definition a prime number is one 
with exactly two positive divisors, itself and one. The number one has only one 
positive divisor.


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## Strange Magic (Sep 14, 2015)

The number 1 is not a prime. A way of looking at numbers is to consider them as products of increasing numbers of factors, "dimensions", if you will. Each such dimension has as its first member a power of 2. Thus, the primes, having no factors other than themselves, are one-dimensional numbers whose first member is 2 to the first power. The next family of numbers are the two-dimensional: 4, 6, 9, etc., all being squares of primes or the products of 2 primes. The first two-dimensional number is 2 squared. Similarly, the three-dimensional numbers begin with 2 cubed (8) and include 12, 18, 20, 27, etc. Same logic for fourth-dimensional numbers; those begin with 2 to the 4th (16). So, by this analysis, 1 is not prime; it is rather the one and only zero-dimensional number, 2 to the zero power, or one. Needless to say, there are infinitely many dimensions, all of whose first members are the ascending integer powers of 2.

The number of primes less than X is best approximated by X divided by (its natural logarithm minus one). There ought to be similar formulas to approximate the number of any body of numbers of any dimension less than X. If found, any number X could then be shown to be the sum of the numbers less than X of all constituent dimensions, beginning with 1. The final goal will be an infinite series beginning with 1 and thus defining X as the sum of that series. I'm no mathematician, so someone with a bigger brain and computer skills can solve this challenge. Let us know how it's going!


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## musicrom (Dec 29, 2013)

No, for the simple fact that we want numbers to have a unique factorization into primes. If 1 was a prime number, this factorization would no longer be unique. 10 = 2*5 = 1*2*5 = 1*1*2*5 = 1*1*1*2*5 = ...


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## ldiat (Jan 27, 2016)

ArtMusic said:


> 1 is an odd number. That's a fact.


gee i must be #1 person as all call me ODD


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## Manxfeeder (Oct 19, 2010)

One is prime if it is followed by the word rib, as in "One prime rib, please."


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