What is the largest bi-truncatable prime?
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What is the largest bi-truncatable prime?
1–10 of 21 posts
Re: What is the largest bi-truncatable prime?
#2Am I overlooking something, or is it obvious that if this is the single largest bi-truncatable prime known so far, that any larger one has to contain this prime in its middle?
So finding a new largest bi-truncatable prime is just a matter of trying to add each single digit at both sides of this prime; if any of them is again a prime, we have a new largest and if none of them is (which I guess is the case because the author must have tried this out already), then there exists no larger bi-truncatable prime.
Re: What is the largest bi-truncatable prime?
#3Am I overlooking something, or is it obvious that if this is the single largest bi-truncatable prime known so far, that any larger one has to contain this prime in its middle? So finding a new largest bi-truncatable prime is just a matter of trying to add each single digit at both sides of this prime; if any of them is again a prime, we have a new largest and if none of them is (which I guess is the case because the…
I would say so, too. Given there are no bi-truncatable primes with length 99, there cannot be any larger ones.
Re: What is the largest bi-truncatable prime?
#4Am I overlooking something, or is it obvious that if this is the single largest bi-truncatable prime known so far, that any larger one has to contain this prime in its middle? So finding a new largest bi-truncatable prime is just a matter of trying to add each single digit at both sides of this prime; if any of them is again a prime, we have a new largest and if none of them is (which I guess is the case because the…
If by "this" you mean the 83-digit prime in the question, then no. There's no indication that there are no other 83-digit bitruncatable primes - that's just the only one the author had found.
If you mean the sole 97-digit solution given in the comments, the implication that all the bitruncatable primes have been found and enumerated by your method, and the assertion that there are no such 99-digit primes - then yes, that looks pretty legit, though I'd want to see an independent verification before accepting it as a proof, since computer programs have bugs.
Re: What is the largest bi-truncatable prime?
#5Am I overlooking something, or is it obvious that if this is the single largest bi-truncatable prime known so far, that any larger one has to contain this prime in its middle? So finding a new largest bi-truncatable prime is just a matter of trying to add each single digit at both sides of this prime; if any of them is again a prime, we have a new largest and if none of them is (which I guess is the case because the…
Yes, you're overlooking something. Look at the 61-digit prime, 9968667351197964859567689459993713773777797133337931717971339. 99% of all 61-digit primes are less than that prime. The 63-digit prime above it prepends a '2' and appends a '7'. If any of the 99% of 61-digit primes less than that prime prepend any digit between 3 and 9 while remaining bitruncatable, then they would be a bigger 63-digit prime.
There's no guarantee that the biggest N+2 digit prime comes from the biggest N digit prime. It could come from the smallest N digit prime if that's the only N digit prime that becomes an N+2 digit prime by prepending a 9.
Re: What is the largest bi-truncatable prime?
#6I find it difficult be interested in these, primes are primes; bi-truncatable are base-10 specific. It feels more like numerology in the same way that we assign meaning to powers of 10 and the natural world does not.
Re: What is the largest bi-truncatable prime?
#7Am I overlooking something, or is it obvious that if this is the single largest bi-truncatable prime known so far, that any larger one has to contain this prime in its middle? So finding a new largest bi-truncatable prime is just a matter of trying to add each single digit at both sides of this prime; if any of them is again a prime, we have a new largest and if none of them is (which I guess is the case because the…
If by "this" you mean the 83-digit prime in the question, then no. There's no indication that there are no other 83-digit bitruncatable primes - that's just the only one the author had found. If you mean the sole 97-digit solution given in the comments, the implication that all the bitruncatable primes have been found and enumerated by your method, and the assertion that there are no such 99-digit primes - then yes,…
I've written some simple code and verified that commenter's numbers through 19 digits.
Edit: parallelized the code and proved through 19 digits. That's where I'm stopping due to the uint64 space limitations.
Re: What is the largest bi-truncatable prime?
#8Am I overlooking something, or is it obvious that if this is the single largest bi-truncatable prime known so far, that any larger one has to contain this prime in its middle? So finding a new largest bi-truncatable prime is just a matter of trying to add each single digit at both sides of this prime; if any of them is again a prime, we have a new largest and if none of them is (which I guess is the case because the…
I would say so, too. Given there are no bi-truncatable primes with length 99, there cannot be any larger ones.
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Re: What is the largest bi-truncatable prime?
#9I find it difficult be interested in these, primes are primes; bi-truncatable are base-10 specific. It feels more like numerology in the same way that we assign meaning to powers of 10 and the natural world does not.
"What's the smallest power of pi that spells your name when encoded in base64?"
Re: What is the largest bi-truncatable prime?
#10I find it difficult be interested in these, primes are primes; bi-truncatable are base-10 specific. It feels more like numerology in the same way that we assign meaning to powers of 10 and the natural world does not.
"What's the smallest power of pi that spells your name when encoded in base64?"
There's probably an infinite set of such powers inside any neighborhood of zero.