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Sequence of 30 primes (curio submission)

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  • James Merickel
    Hi, folks.  Just wanted to inform you all of a little thing I have computed:   16072758981106442684006718854529251552093=  
    Message 1 of 1 , Feb 7, 2013
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      Hi, folks.  Just wanted to inform you all of a little thing I have computed:
       
      16072758981106442684006718854529251552093=
       
      abcdef+(1/a+1/b+1/c+1/d+1/e+1/f)*109#, where
       
      a=7*13*37*83, b=17*19*89, c=11*79*101, d=23*29*67*103, e=47*61*107 and f=41*53*109.
       
      Uniquely, it is the last of 30 primes beginning with 7=1+1+1+1+1+1+1 produced by sequentially multiplying all but one addend by the primes from 2 through 109.
       
      The sequential build-up can be obtained from 485191936591420718030369 (just the smallest of 62 primes that work) by looking at the number's base-7 representation and taking the digits by order of increasing significance as the addend not to be multiplied by a prime (Digit equal to 0 means the 1st addend is skipped and the rest multiplied by the prime, etc., with the units digit corresponding to the prime 2).
       
      Jim Merickel
      P.S.  Note that with the strict requirement that a term composed of one 1 and the rest of the addends 2 be prime would make the start of any larger analogous sequence start with at least 19.  I doubt such a maximal sequence can be found for so large a start, but I will try to see if I am wrong. 

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