Number of primes  k · 2n + 1  for odd  k,  1 ≤ k < 1200
 
n   primes  
1−1000   8010  
1001−2000 1216  
2001−3000 684  
3001−4000 488  
4001−5000 334  
5001−6000 309  
6001−7000 285  
7001−8000 232  
8001−9000 203  
  9001−10000   183  
total 11944  
     
n   primes  
1−10000   11944  
10001−20000 1215  
20001−30000 721  
30001−40000 458  
40001−50000 372  
50001−60000 292  
60001−70000 298  
70001−80000 231  
80001−90000 188  
  90001−100000   157  
total 15876  
     
n   primes  
1−100000   15876  
100001−200000 1214  
200001−300000 693  
300001−400000 510  
400001−500000 398  
500001−600000 319  
600001−700000 255  
700001−800000 230  
800001−900000 214  
  900001−1000000   188  
total 19897  

n   primes  
  n = 1000001−1100000     167  
  n = 1100001−1200000     160  
  n = 1200001−1300000     153  
  n = 1300001−1400000     129  
  n = 1400001−1500000     126  
  n = 1500001−1600000     101  
  n = 1600001−1700000     109  
  n = 1700001−1800000     120  
  n = 1800001−1900000     94  
  n = 1900001−2000000     85  
total   1244  
     
n   primes  
  n = 2000001−2100000     104  
  n = 2100001−2200000     89  
  n = 2200001−2300000     84  
  n = 2300001−2400000     68  
  n = 2400001−2500000     73  
  n = 2500001−2600000     55  
  n = 2600001−2700000     65  
  n = 2700001−2800000     64  
  n = 2800001−2900000     76  
  n = 2900001−3000000     54  
total   732  
     
n   primes  
  n = 3000001−3100000     59  
  n = 3100001−3200000     45  
  n = 3200001−3300000     49  
  n = 3300001−3400000     53  
  n = 3400001−3500000     43  
  n = 3500001−3600000     44  
total   293  

Number of primes  k · 2n + 1  for odd  k,  1200 < k < 10000
 
n   primes  
1−1000   55466  
1001−2000 8685  
2001−3000 5137  
3001−4000 3622  
4001−5000 2897  
5001−6000 2231  
6001−7000 1952  
7001−8000 1668  
8001−9000 1432  
  9001−10000   1380  
total 84470  
     
n   primes  
1−10000   84470  
10001−20000 8800  
20001−30000 5225  
30001−40000 3562  
40001−50000 2792  
50001−60000 2330  
60001−70000 1944  
70001−80000 1714  
80001−90000 1514  
  90001−100000   1420  
total   113771  
     
n   primes  
1−100000   113771  
100001−200000 8924  
200001−300000 5182  
300001−400000 3729  
400001−500000 2783  
500001−600000 2336  
600001−700000 1900  
700001−800000 1630  
800001−900000 1495  
  900001−1000000   1317  
total   143067  

     
n   primes  
  1000001−1100000   1247  
  1100001−1200000   1074  
  1200001−1300000   1050  
  1300001−1400000   956  
  1400001−1500000   873  
  1500001−1600000   813  
  1600001−1700000   811  
  1700001−1800000   690  
  1800001−1900000   684  
total   8198  

Number of primes  k · 2n + 1  for odd  k,  10000 < k < 100000
 
n   primes  
1−1000   538541  
1001−2000 88854  
2001−3000 51744  
3001−4000 37387  
4001−5000 28480  
5001−6000 23608  
6001−7000 19730  
7001−8000 17101  
8001−9000 15053  
  9001−10000   13640  
total 834138  
     
n   primes  
1−10000   834138  
10001−20000 89966  
20001−30000 52707  
  30001−40000   37353  
40001−50000 28830  
50001−60000 23482  
total   1066476  

Number of primes  k · 2n + 1  for odd  k,  10000 · (r − 1) < k < 10000 · r
and for all 1 ≤ n ≤ 10000

 
r = 1 r = 2 r = 3 r = 4 r = 5 r = 6 r = 7 r = 8 r = 9 r = 10
  96414     94447     93501     92665     93006     92569     91978     92611    91558     91803  

  Total number for all  k < 100000     930552 primes  


Extended version of March 11, 2024.
Corrected April 16, November 27 and December 12, 2023;
January 9, 2024.
See also Search and Double-Check Status.

Compact lists of primes are available for 
            1 ≤ k < 1200,                1 ≤ n ≤  100000     (
15876 primes) 
            1 < k < 1200,      100000 < n ≤ 1000000      (4021 primes) 
            1 < k < 1200,    1000000 < n ≤ 3600000      (2269 primes)

      1200 < k < 10000,              1 ≤ n ≤  100000   (113771 primes) 
      1200 < k < 10000,    100000 < n ≤ 1000000    (29296 primes)  
      1200 < k < 10000,  1000000 < n ≤ 1800000      (8198 primes)

    10000 < k < 100000,            1 ≤ n ≤  10000     (834138) primes  
    10000 < k < 100000,    10000 < n ≤  60000     (232338) primes)

Also available: 
      1200 < k < 10000,  3322000 < n < 3486000    (613 megaprimes)