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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.

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