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 8934   200001−300000 5182   300001−400000 3729   400001−500000 2784   500001−600000 2336   600001−700000 1900   700001−800000 1630   800001−900000 1495     900001−1000000   1317   total   143078

n   primes     1000001−1100000   1247     1100001−1200000   1075     1200001−1300000   1050     1300001−1400000   956     1400001−1500000   873     1500001−1600000   813     1600001−1700000   811     1700001−1800000   690     1800001−1900000   684     1900001−2000000   646   total   8845

n   primes     2000001−2100000   637     2100001−2200000   611     2200001−2300000   576   total   1824

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   60001−70000 19936   70001−80000 17514   80001−90000 15276     90001−100000   13707   total   1132909

n   primes   1−100000   1132909     100001−110000   12545   110001−120000 11298   120001−130000 10266   130001−140000 9652   140001−150000 9008   total   52769

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 July 7, 2024, updated March 5, April 20,
April 28, May 14, June 12, July 25, August 28 and
September 22, 2025.
Corrected April 16, November 27 and December 12, 2023;
January 9, August 9, August 23, and September 8, 2024;
February 12, 2025.
See also Search and Double-Check Status.

Compact lists of primes are available for the following ranges. 
            1 ≤ k < 1200,                1 ≤ n ≤  100000     (15876 primes)  
            1 < k < 1200,      100000 < n ≤ 1000000      (4021 primes) 
            1 < k < 1200,    1000000 < n ≤ 3600000      (2269 primes) 
            1 < k < 1200,    3600000 < n       Currently known primes

      1200 < k < 10000,              1 ≤ n ≤  100000   (113771 primes) 
      1200 < k < 10000,    100000 < n ≤ 1000000    (29307 primes)  
      1200 < k < 10000,  1000000 < n ≤ 2300000    (10669 primes) 
      1200 < k < 10000,  2300000 < n       Currently known primes 
      1200 < k < 10000,  3322000 < n < 3486000   (613 megaprimes) 

    10000 < k < 100000,            1 ≤ n ≤  10000     (834138 primes)  
    10000 < k < 100000,    10000 < n ≤  100000   (298771 primes)  
    10000 < k < 100000,  100000 < n ≤  150000     (52769 primes)

Also available, but not included in the statistics above: 
    10000 < k < 30000,    150000 < n ≤ 1000000    (54331 primes) 
    30000 < k < 70000,    150000 < n ≤  400000     (56842 primes) 
    10000 < k < 100000,  150000 < n       Currently known primes 

The above compact lists include  772023  primes with less than 1000
digits and a total of  701354  titanic primes.