Snowball Prime Numbers #shorts

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If we count 1 as a prime digit, you can start with 1, 2, 3, 5, or 7 and build Snowball Primes -- prime numbers that remain prime each time you add another digit. Start with 3? Add a 1, still prime. Start with 7? Add a 3, still prime. 73, add a 1? 731 -- STILL PRIME.

In just a few hours, you can build the entire roster of Snowball Primes up to 8 digits by hand. DO IT. Why not? This is recreational math. Your parents will be proud of you.

#vsauce #maths #education

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mathematicians having fun in their free time

novm

Important note: the number 2 is the most useless prime number for a snowball prime, since you can only use it as the first number.

9, on the other hand, is the opposite. It can be used in a snowball prime but it can never start it.

alien_in_white_

If you're wondering why there's no 5 it's because if 5 was added then it would be divisible by 5, which isn't prime

Zettabyte

Have we found the biggest snowball prime yet?

thelordclarkson

3072th prime:
2: Prime
28: Composite
281: Prime
2818: Composite
28181: Prime

Farzriyaz

the snow is moist, perfect for constructing the perfect snowball. but what's this? a seven made out of snow?! you carefully pick up the seven, and stare directly at it. something is off, but you can't tell what. suddenly, it hits you. that's not snow, it's ice. you realise what you're holding, and try to put it back, but to no avail, as your hand has been frozen in an awkward position. you call for help, but unfortunately for you, no-one is there. your joints cry out in pain as the seven contorts your hand into the shape of a three. after what feels like weeks, the three that was once your hand detaches from your frost bitten wrist. you make an attempt to flee, but the seventy-three knows your every move. and soon you are buried under a mountain of snow.

omatic_opulis

I give up. WAAAAY too many people dont understand the difference between number and digit 🤣 So many complaints about 9 😂😂😂

toolebukk

Thank you for a fun simple math lecture that I liked so much!

DavidmamaTheHFanatic

Fun fact: there is only a finite number of these kinds of primes, and there are 83 of them.

bagelnine

This has me wondering what the largest known prime snowball is.

weelusmallgi

0, 4, 6, 8 can't be used anywhere
2, 5 can't be used anywhere except as the first number
This means that only 1, 3, 7 and 9 can be used to continue your snowball

vincenzodanello

Why does he regularly consider 1 a prime. It just isn't a prime.

VillagerJeff

1 really shouldn't be considered a prime. It doesn't have 2 factors like a prime number; it only has a single factor. Also, in ring theory, 1, -1, i, -i, and a bunch of other similar elements are often called _units_, which are elements with a multiplicative inverse (in a particular number system). They are grouped together, and they behave very differently from primes, irreducibles, and composites.

As an analogy, consider the polynomial x^2-1. By difference of squares, we can factor this polynomial as (x-1)(x+1). However, we can also factor it as (1/2)(2x^2-2), but this factorization _feels_ different. The reason is because you can factor 1/2 out of any polynomial, but you can't always factor out x-1 or x+1. With real numbers (or rationals, or complex numbers, or any field) 1/2 is a unit, but nonconstant polynomials are not units. In the same way, we could factor 6 as 2*3, but we could also factor it as (-1)(-6).

tl;dr 1 is a unit, and shouldn't be categorized with the primes or composites. Just like -1 for the integers, or nonzero constants for polynomials.

JM-usfr