# 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](https://oeis.org/search?q=primecount&language=english&go=Search).
There is also a [mersenneforum thread](https://www.mersenneforum.org/showthread.php?t=20473)
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. Please note that most of these records
have been computed using the
[primecount version with backup support](https://github.com/kimwalisch/primecount/tree/backup3#primecount-backup)
as these record computations often take weeks or months to complete and power
outage(s) may occur in such time frames.

## [A006880](https://oeis.org/A006880) records

<table>
  <tr align="center">
    <td><b>x</b></td>
    <td><b>Number of primes ≤ 10<sup>n</sup></b></td>
    <td><b>Date</b></td>
    <td><b>Computed by</b></td>
  </tr>
  <tr align="right">
    <td>10<sup>27</sup></td>
    <td>16,352,460,426,841,680,446,427,399</td>
    <td>2015-09-06</td>
    <td>Kim Walisch & David Baugh</td>
  </tr>
  <tr align="right">
    <td>10<sup>28</sup></td>
    <td>157,589,269,275,973,410,412,739,598</td>
    <td>2020-08-30</td>
    <td>Kim Walisch & David Baugh</td>
  </tr>
</table>

For verification, all results on this page have been computed twice using
different alpha tuning parameters (configuration parameters).
PrimePi(10<sup>28</sup>) was successfully verified on the 27th October 2020.
You can read our initial PrimePi(10<sup>28</sup>) announcement and the  
successful verification announcement in our
[mersenne forum thread](https://mersenneforum.org/showthread.php?t=20473&page=3).

## [A006988](https://oeis.org/A006988) records

<table>
  <tr align="center">
    <td><b>x</b></td>
    <td><b>10<sup>n</sup>-th prime</b></td>
    <td><b>Date</b></td>
    <td><b>Computed by</b></td>
  </tr>
  <tr align="right">
    <td>10<sup>23</sup></td>
    <td>5,596,564,467,986,980,643,073,683</td>
    <td>2015-10-09</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>10<sup>24</sup></td>
    <td>58,310,039,994,836,584,070,534,263</td>
    <td>2015-10-20</td>
    <td>David Baugh</td>
  </tr>
</table>

## [A007053](https://oeis.org/A007053) records

<table>
  <tr align="center">
    <td><b>x</b></td>
    <td><b>Number of primes ≤ 2<sup>n</sup></b></td>
    <td><b>Date</b></td>
    <td><b>Computed by</b></td>
  </tr>
  <tr align="right">
    <td>2<sup>87</sup></td>
    <td>2,610,087,356,951,889,016,077,639</td>
    <td>2018-11-28</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>2<sup>88</sup></td>
    <td>5,159,830,247,726,102,115,466,054</td>
    <td>2019-01-05</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>2<sup>89</sup></td>
    <td>10,201,730,804,263,125,133,012,340</td>
    <td>2020-05-09</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>2<sup>90</sup></td>
    <td>20,172,933,541,156,002,700,963,336</td>
    <td>2020-10-07</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>2<sup>91</sup></td>
    <td>39,895,115,987,049,029,184,882,256</td>
    <td>2020-11-14</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>2<sup>92</sup></td>
    <td>78,908,656,317,357,166,866,404,346</td>
    <td>2020-12-02</td>
    <td>David Baugh</td>
  </tr>
</table>

## [A040014](https://oeis.org/A040014) records

<table>
  <tr align="center">
    <td><b>x</b></td>
    <td><b>Number of primes < e<sup>n</sup></b></td>
    <td><b>Date</b></td>
    <td><b>Computed by</b></td>
  </tr>
  <tr align="right">
    <td>e<sup>48</sup></td>
    <td>14,936,302,130,478,888,296</td>
    <td>2015-03-07</td>
    <td>David Baugh</td>
  </tr>
    <tr align="right">
    <td>e<sup>49</sup></td>
    <td>39,754,427,477,873,197,008</td>
    <td>2015-03-07</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>e<sup>50</sup></td>
    <td>105,856,368,969,311,706,141</td>
    <td>2015-03-07</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>e<sup>51</sup></td>
    <td>281,987,525,487,483,629,729</td>
    <td>2015-03-07</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>e<sup>52</sup></td>
    <td>751,479,276,811,434,164,860</td>
    <td>2015-03-10</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>e<sup>53</sup></td>
    <td>2,003,417,881,848,387,803,588</td>
    <td>2015-03-25</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>e<sup>54</sup></td>
    <td>5,343,023,851,430,824,336,740</td>
    <td>2015-04-10</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>e<sup>55</sup></td>
    <td>14,254,686,649,867,417,156,723</td>
    <td>2015-05-17</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>e<sup>56</sup></td>
    <td>38,043,242,922,236,683,117,535</td>
    <td>2015-08-03</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>e<sup>57</sup></td>
    <td>101,564,348,447,358,891,206,901</td>
    <td>2015-09-08</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>e<sup>58</sup></td>
    <td>27,123,381,893,146,940,4637,903</td>
    <td>2016-08-24</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>e<sup>59</sup></td>
    <td>724,569,999,669,566,733,678,976</td>
    <td>2020-08-04</td>
    <td>David Baugh</td>
  </tr>
  <tr align="right">
    <td>e<sup>60</sup></td>
    <td>1,936,182,213,929,180,232,892,229</td>
    <td>2020-10-22</td>
    <td>David Baugh</td>
  </tr>
</table>

## [A122121](https://oeis.org/A122121) records

<table>
  <tr align="center">
    <td><b>x</b></td>
    <td><b>Number of primes ≤ 10<sup>n/2</sup></b></td>
    <td><b>Date</b></td>
    <td><b>Computed by</b></td>
  </tr>
  <tr align="right">
    <td>10<sup>47/2</sup></td>
    <td>5,956,317,545,928,249,075,039</td>
    <td>2015-02-23</td>
    <td>David Baugh</td>
  </tr>
    <tr align="right">
    <td>10<sup>49/2</sup></td>
    <td>57,086,403,558,149,290,301,868</td>
    <td>2015-04-27</td>
    <td>David Baugh</td>
  </tr>
    <tr align="right">
    <td>10<sup>51/2</sup></td>
    <td>548,074,549,053,620,897,173,483</td>
    <td>2015-06-18</td>
    <td>David Baugh</td>
  </tr>
    <tr align="right">
    <td>10<sup>53/2</sup></td>
    <td>5,270,353,162,790,246,525,701,178</td>
    <td>2016-08-31</td>
    <td>David Baugh</td>
  </tr>
</table>