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24117Re: 13-chains of consecutive smooth numbers

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  • Jim White
    Mar 5, 2012
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      Andrey's chain puzzle is interesting.  Could it be
      he already has found the maximum possible result
      for chain length 13?
       
      It's hard to see how that result can be beaten.
       
      Some results with weights of 2.2 or more:
       
          28246112570058, weight = 2.2053 (P =  1257251)
          18911412089528, weight = 2.2077 (P =  1032307)
         218381019281507, weight = 2.2410 (P =  2504167)
           9288363679368, weight = 2.2480 (P =   587149)
        3393509932556102, weight = 2.2536 (P =  7788997)
        4532039198639948, weight = 2.2536 (P =  8856259)
        4532039198639949, weight = 2.2536 (P =  8856259)
       12469670986534198, weight = 2.2547 (P = 13762769)
       10160468895884110, weight = 2.2592 (P = 12163843)
         461881571558141, weight = 2.2615 (P =  3050603)
        7909529450841510, weight = 2.2621 (P = 10669823)
         211814723372355, weight = 2.2918 (P =  1782043)
         430753934627814, weight = 2.4217 (P =  1103933)

      Perhaps the 14-chain at N = 4532039198639948 might
      be a good result? What are the best known results
      for 14 or longer chains?


      ________________________________
      From: Andrey Kulsha <Andrey_601@...>
      To: PrimeNumbers@...
      Sent: Sunday, 4 March 2012, 9:53
      Subject: Re: [PrimeNumbers] Two large consecutive smooth numbers


       

      > Puzzle: find a chain of 13 consecutive p-smooth integers,
      > starting at N, with log(N)/log(p) greater than
      >
      > log(8559986129664)/log(58393) = 2.71328

      Best regards,

      Andrey




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