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 = 3000001−3100000     59     n = 3100001−3200000     45     n = 3200001−3300000     49     n = 3300001−3400000     53     n = 3400001−3500000     43     n = 3500001−3600000     44

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 1498     90001−100000   1419   total   113754

n   primes   1−100000   113754   100001−200000 8928   200001−300000 5198   300001−400000 3729   400001−500000 2779   500001−600000 2336   600001−700000 1900   700001−800000 1630   800001−900000 1495     900001−1000000   1317   total   143066         1000001−1100000   1247     1100001−1200000   1074     1200001−1300000   1050     1300001−1400000   956     1400001−1500000   873     1500001−1600000   813

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     92609     91558     91803

Total number for all  k < 100000     930550 primes

Slightly extended version of August 30, 2022.
See also Search and Double-Check Status.