# Records set using primecount

Below is a selection of records that have been computed using primecount. For a more complete list search for primecount on OEIS.org. There is also a mersenneforum thread where we have announced important records as well as details about these computations. If you have used primecount to compute an important new record please let me know and I will add your record to this page.

Most of these records have been computed using the primecount app with backup support (which I stopped maintaining due to lack of time) as these record computations often take weeks or months to complete and power outages may occur in such time frames. Since the latest primecount-7.x is significantly faster than the last primecount-backup-6.4 (especially on servers with > 100 CPU cores), I suggest using the latest primecount version without backup support if you have a good uninterruptible power supply (UPS) which prevents most power outages of your PC/server. You can use the primecount app together with the Unix `tee` command to store intermediate results in a log file.

# Double checking π(x) computations

For large π(x) computations that run over several weeks or months, it is important to verify such computations to protect against miscalculations due to hardware errors and/or bugs in primecount.

To verify a π(x) computation, you compute π(x) twice. But for the second run you use the `--double-check` option. The `--double-check` option enables the use of alternative alpha tuning factors, ensuring that all internal bounds in the second computation differ slightly from the first run. This redundancy helps guard against potential bugs in primecount: if an error exists, it is highly unlikely that both π(x) computations would produce the same (incorrect) result.

    # First pi(x) computation using default alpha tuning factors
    $ primecount 1e20 --status

    # Second pi(x) computation using alternative alpha tuning factors
    $ primecount 1e20 --status --double-check

# A006880 records

x | Number of primes ≤ 10n | Date | Computed by
1027 | 16,352,460,426,841,680,446,427,399 | 2015-09-06 | Kim Walisch & David Baugh
1028 | 157,589,269,275,973,410,412,739,598 | 2020-08-30 | Kim Walisch & David Baugh
1029 | 1,520,698,109,714,272,166,094,258,063 | 2022-02-28 | Kim Walisch & David Baugh

For verification, all results on this page have been computed twice using different alpha tuning parameters (configuration parameters). You can read our announcements of these results in our mersenne forum thread.

# A006988 records

x | 10n-th prime | Date | Computed by
1023 | 5,596,564,467,986,980,643,073,683 | 2015-10-09 | David Baugh
1024 | 58,310,039,994,836,584,070,534,263 | 2015-10-20 | David Baugh
1025 | 606,527,267,811,189,857,426,370,533 | 2022-04-07 | David Baugh

# A007053 records

x | Number of primes ≤ 2n | Date | Computed by
287 | 2,610,087,356,951,889,016,077,639 | 2018-11-28 | David Baugh
288 | 5,159,830,247,726,102,115,466,054 | 2019-01-05 | David Baugh
289 | 10,201,730,804,263,125,133,012,340 | 2020-05-09 | David Baugh
290 | 20,172,933,541,156,002,700,963,336 | 2020-10-07 | David Baugh
291 | 39,895,115,987,049,029,184,882,256 | 2020-11-14 | David Baugh
292 | 78,908,656,317,357,166,866,404,346 | 2020-12-02 | David Baugh

# A040014 records

x | Number of primes < en | Date | Computed by
e48 | 14,936,302,130,478,888,296 | 2015-03-07 | David Baugh
e49 | 39,754,427,477,873,197,008 | 2015-03-07 | David Baugh
e50 | 105,856,368,969,311,706,141 | 2015-03-07 | David Baugh
e51 | 281,987,525,487,483,629,729 | 2015-03-07 | David Baugh
e52 | 751,479,276,811,434,164,860 | 2015-03-10 | David Baugh
e53 | 2,003,417,881,848,387,803,588 | 2015-03-25 | David Baugh
e54 | 5,343,023,851,430,824,336,740 | 2015-04-10 | David Baugh
e55 | 14,254,686,649,867,417,156,723 | 2015-05-17 | David Baugh
e56 | 38,043,242,922,236,683,117,535 | 2015-08-03 | David Baugh
e57 | 101,564,348,447,358,891,206,901 | 2015-09-08 | David Baugh
e58 | 27,123,381,893,146,940,4637,903 | 2016-08-24 | David Baugh
e59 | 724,569,999,669,566,733,678,976 | 2020-08-04 | David Baugh
e60 | 1,936,182,213,929,180,232,892,229 | 2020-10-22 | David Baugh
e61 | 5,175,318,892,686,816,487,170,078 | 2021-03-15 | David Baugh
e62 | 13,837,220,920,267,326,266,315,383 | 2022-04-11 | David Baugh

# A122121 records

x | Number of primes ≤ 10n/2 | Date | Computed by
1047/2 | 5,956,317,545,928,249,075,039 | 2015-02-23 | David Baugh
1049/2 | 57,086,403,558,149,290,301,868 | 2015-04-27 | David Baugh
1051/2 | 548,074,549,053,620,897,173,483 | 2015-06-18 | David Baugh
1053/2 | 5,270,353,162,790,246,525,701,178 | 2016-08-31 | David Baugh