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The way I understand this concept of a 'widely digitally delicate prime' is that you can take such a prime, prepend it with any sequence, and receive a prime in
by Cogito 6y ago
The way I understand this concept of a 'widely digitally delicate prime' is that you can take such a prime, prepend it with any sequence, and receive a prime in return.
If that is the case, then finding such a number immediately trivialises the search for the 'largest known prime' - take the largest known prime, tack this number on the back of it, and you now have a new largest prime. I guess you'd get bonus points if somehow it's also Mersenne.
- stochastastic 6y agoI think it’s the other way around — tack this number on the back of anything and the result is composite.
- Cogito 6y agoAh of course and that makes far more sense. Adding this prime to the end of a number guarantees a composite. I wonder if that is a property the belongs to primes, or if there are non-trivial composite examples (any number ending in 2 has this property).
- bodhiandpysics1 6y agoYou can rephrase that conjecture to say... given any sequence of digits not ending in 2 (or 0), is there a prime number that ends in that sequence. That's an interesting conjecture!
- bodhiandphysics 6y agoAcchhh!!! Brain fart!!!
- Cogito 6y agoyes I like that phrasing. Similarly we can say there is a class of primes that have this property, what other classes of numbers also have this property?
- avz 6y ago> this concept of a 'widely digitally delicate prime' is that you can take such a prime, prepend it with any sequence, and receive a prime in return. This makes no sense. Let X be a number that satisfies your condition and consider the number XX formed prepending X to itself. You're asserting that XX is prime, but it is obviously composite, because it is divisible by X (just like say 2929 is 29*101).