20131226, 21:40  #1 
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
2^{5}·11·17 Posts 
Euclid Mullin
Recently I wrote a program that produced the Euclid mullin sequence with different starting values. I was interested in whether different starting values would allow more consecutive primes to be found than the standard sequence. Using both +1 and 1 I found sequences with all the primes upto 67 for +1 and 53 for 1.
For +1: 53 For 1: 137 In terms of factoring I followed the following rules: trial factor upto 1e6 If a factor was found I know it is the smallest so move on to next iteration. ecm to 20, 25, and 30 digits Once 30 digits ecm was run I would assume that if the smallest known factor is prime and less than 30*0.8=24 digits it was the smallest and continue. The chance of a mistake here is very small. I manually added a few factors of composites <90 digits. Searching upto a starting value of 1000 with ecm only upto 20 digits for both +1 and 1 I found the 1 sequence starting at 457 has all primes upto 67 so increasing the starting value further can be useful. Is anyone interested in these results? Does anyone want to help extend any of these sequences? I have attached the results upto 200 on both sides. All composites have c before them. Last fiddled with by henryzz on 20131226 at 22:09 
20131227, 01:37  #2 
I moo ablest echo power!
May 2013
2^{2}×449 Posts 
I can't do anything at the moment (visiting my parents for Christmas and New Year's), but I'd be happy to help explore/expand things when I get back (flying back Jan. 3rd).

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