20151224, 01:04  #397 
Sep 2006
The Netherlands
2AE_{16} Posts 
k=733 , searched to n=4 million. Busy searching up to 5M. No new primes so far.
Hopefully more luck next year (or in the few days remaining of this year). 
20160101, 23:03  #398 
Apr 2010
Over the rainbow
4644_{8} Posts 
fermat,
20160101*2^n+1.... prime found so far : 20160101*2^5867+1 20160101*2^19977+1 20160101*2^21207+1 20160101*2^24393+1 20160101*2^27869+1 20160101*2^93615+1 20160101*2^98883+1 20160101*2^137747+1 20160101*2^169797+1 20160101*2^194597+1 
20160215, 11:25  #399 
Sep 2006
The Netherlands
2·7^{3} Posts 

20170516, 16:05  #400 
"Vasiliy"
Apr 2017
Ukraine
60_{10} Posts 
k=6371 from n=10000 to 100000
Found 1 prime: 6371*2^623181 is prime! (18764 decimal digits) 
20170620, 03:37  #401 
"Curtis"
Feb 2005
Riverside, CA
2×7×11×29 Posts 
I filled some gaps recently on old old work, and found:
2115*2^6073901 is prime. I'll report completion status on the k>300 (choose your own k) thread. Last fiddled with by VBCurtis on 20170620 at 03:37 
20170829, 00:55  #402 
"Dylan"
Mar 2017
2^{4}·3·11 Posts 
I have searched k = 17849 to a maximum n value of 1 M (starting from n =1), and the following primes were found:
17849*2^54481 (already found by Gallot) 17849*2^298401 17849*2^2789121 Residue file is attached: 
20170923, 20:16  #403 
"Dylan"
Mar 2017
2^{4}·3·11 Posts 
I have searched k = 17851 to n = 500k (starting from n =1), and the following primes were found:
17851*2^51 17851*2^171 17851*2^611 17851*2^1211 17851*2^5291 17851*2^9071 17851*2^11411 17851*2^16691 17851*2^50531 17851*2^50811 17851*2^122471 17851*2^403991 17851*2^426411 17851*2^456791 17851*2^724451 17851*2^1032731 17851*2^1699611 17851*2^2801111 17851*2^3204131 Residue file is attached: 
20200202, 14:19  #404 
Random Account
Aug 2009
U.S.A.
11010001110_{2} Posts 
1901*2^1958701 is prime! (58967 decimal digits).
1901*2^2390301 is prime! (71959 decimal digits) 1901*2^3350181 is prime! (100854 decimal digits) Passed 350,000. Heading somewhere above 1,200,000 most likely. Residue file attached. Last fiddled with by storm5510 on 20200202 at 14:29 Reason: Additional 
20200205, 00:41  #405 
Random Account
Aug 2009
U.S.A.
2×839 Posts 
k = 1901, n = 700K complete. Continuing...
srsieve / sr1sieve / llr No new primes found. Residues attached. 
20200206, 16:45  #406 
Random Account
Aug 2009
U.S.A.
3216_{8} Posts 
k = 1901, n = 800K complete. Continuing...
srsieve / sr1sieve / llr No new primes found. Residues attached. 
20200208, 02:42  #407 
Random Account
Aug 2009
U.S.A.
11010001110_{2} Posts 
If I read it right, the smallest value in the top 5000 list has 429,390 digits. Why separate ones larger here?

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