Re: isprime of flattened primes...

On 21 Apr 2006 23:04:23 GMT, rusin@xxxxxxxxxxxxxxxxxxxxx (Dave Rusin)
wrote:

In article <eeudnXzMyp2wotTZRVn-iA@xxxxxxxxx>,
Gerard Schildberger <Gerard46@xxxxxxx> wrote:

Consider the number series

where each number is a flattened list of primes (that
is, a list of primes with the blanks removed to form
a single number).

Once you get "past" the single digit primes, should
there be any more primes?

What does "should" mean here? Anyway, Maple reports that

235711131719232931374143475359616771737983899710110310710911312713113713914\
91511571631671731791811911931971992112232272292332392412512572632692712\
77281283293307311313317331337347349353359367373379383389397401409419421\
43143343944344945746146346747948749149950350952152354154755756356957157\
7587593599601607613617619631641643647653659661673677683691701709719
is prime.

However in fairness to the OP, let me point out that the
counterexamples all appear to be rather "small".

Let a_n be the concatenation of the first n primes.

Thus, a = 2, 23, 235, 2357, 235711, 23571113, ...

Conjecture 1: a_n is composite for all sufficiently large n.

Conjecture 2: a_n is composite for all n > 435

quasi
.

Relevant Pages

  • Re: isprime of flattened primes...
    ... Let a_n be the concatenation of the first n primes. ... Conjecture 1: a_n is composite for all sufficiently large n. ...
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  • Re: isprime of flattened primes...
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  • Re: isprime of flattened primes...
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  • Re: Twin prime composites!
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