Question:
Are there infinitely many prime numbers in the Look-and-say sequence?
In the sequence, I found that $11$, $312211$ and $13112221$ are prime numbers.
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1 Answer
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5
Not an answer.
I generated the first $50$ terms of the sequence; it does not take much time. The prime search is another story. Among the first $38$ (above, my computer gave up), as prime numbers, I only found the second and the two you reported.
Congratulations.
answered Jun 9, 2019 at 8:08
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1$\begingroup$ any prime needs certain properties, one of which is the digits that are non zero mod 3, can only exceed the other type of digits non zero mod 3 by a quantity that are 1 or 2 mod 3. $\endgroup$– user645636Commented Jun 9, 2019 at 20:05
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1$\begingroup$ @RoddyMacPhee. I am very bad in number theory, prime numbers (plus many other areas); so, I feel vry dumb when reading your comment. So, taking into account the manner these numbers are generated, do you have any idea about their primilarity ? $\endgroup$ Commented Jun 10, 2019 at 2:26
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1$\begingroup$ no, but if we can check how many 1's versus 2's there are we can limit which iterations we ultimately check for primality. $\endgroup$– user645636Commented Jun 10, 2019 at 9:10
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$\begingroup$ So is this a hypothesis? And could I name it? $\endgroup$– liszt16Commented Jun 16, 2019 at 3:17
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1$\begingroup$ I should not conclude anything. This was just an observation based on the $38$ first terms. May be, looking at his comments, Roddy MacPhee could help. $\endgroup$ Commented Jun 16, 2019 at 3:26