July 1, 2023 Preprint Open Access

Gennady Butov

JSON Export

{
  "conceptdoi": "10.15161/oar.it/77082", 
  "conceptrecid": "77082", 
  "created": "2023-07-01T19:58:09.551308+00:00", 
  "doi": "10.15161/oar.it/77083", 
  "files": [
    {
      "bucket": "8a6cf336-60fa-4cf4-a8f4-cd972e277792", 
      "checksum": "md5:22e48d33ce05dd30365d77302513e1de", 
      "key": "ellipses_hyperbolas_decompositions.pdf", 
      "links": {
        "self": "https://www.openaccessrepository.it/api/files/8a6cf336-60fa-4cf4-a8f4-cd972e277792/ellipses_hyperbolas_decompositions.pdf"
      }, 
      "size": 667120, 
      "type": "pdf"
    }
  ], 
  "id": 77083, 
  "links": {
    "badge": "https://www.openaccessrepository.it/badge/doi/10.15161/oar.it/77083.svg", 
    "bucket": "https://www.openaccessrepository.it/api/files/8a6cf336-60fa-4cf4-a8f4-cd972e277792", 
    "conceptbadge": "https://www.openaccessrepository.it/badge/doi/10.15161/oar.it/77082.svg", 
    "conceptdoi": "https://doi.org/10.15161/oar.it/77082", 
    "doi": "https://doi.org/10.15161/oar.it/77083", 
    "html": "https://www.openaccessrepository.it/record/77083", 
    "latest": "https://www.openaccessrepository.it/api/records/77110", 
    "latest_html": "https://www.openaccessrepository.it/record/77110"
  }, 
  "metadata": {
    "access_right": "open", 
    "access_right_category": "success", 
    "contributors": [
      {
        "name": "Gennady Butov", 
        "type": "Researcher"
      }
    ], 
    "creators": [
      {
        "name": "Gennady Butov"
      }
    ], 
    "description": "<p>This is just an attempt to associate sums or differences of prime numbers with points lying on an ellipse or hyperbola.<br>\nCertain pairs of prime numbers can be represented as radius-distances from the focuses to points lying either on the ellipse or on the hyperbola.<br>\nThe ellipse equation can be written in the following form: |p(k)| + |p(t)| = 2n.<br>\nThe hyperbola equation can be written in the following form: ||p(k)| - |p(t)|| = 2n.<br>\nHere p(k) and p(t) are prime numbers (p(1) = 2, p(2) = 3, p(3) = 5, p(4) = 7,...),<br>\nk and t are indices of prime numbers,<br>\n2n is a given even number,<br>\nk, t, n &isin; N.<br>\nIf we construct ellipses and hyperbolas based on the above, we get the following:<br>\n1) there are only 5 non-intersecting curves (for 2n=4; 2n=6; 2n=8; 2n=10; 2n=16). The remaining ellipses have intersection points.<br>\n2) there is only 1 non-intersecting hyperbola (for 2n=2) and 1 non-intersecting vertical line. The remaining hyperbolas have intersection points.<br>\nWill there be any new thoughts, ideas about this?</p>", 
    "doi": "10.15161/oar.it/77083", 
    "keywords": [
      "prime, primes, number, numbers, even, theory, ellipse, ellipses, hyperbole, hyperboles, decomposition"
    ], 
    "language": "eng", 
    "license": {
      "id": "CC-BY-4.0"
    }, 
    "publication_date": "2023-07-01", 
    "related_identifiers": [
      {
        "identifier": "10.15161/oar.it/77082", 
        "relation": "isVersionOf", 
        "scheme": "doi"
      }
    ], 
    "relations": {
      "version": [
        {
          "count": 2, 
          "index": 0, 
          "is_last": false, 
          "last_child": {
            "pid_type": "recid", 
            "pid_value": "77110"
          }, 
          "parent": {
            "pid_type": "recid", 
            "pid_value": "77082"
          }
        }
      ]
    }, 
    "resource_type": {
      "subtype": "preprint", 
      "title": "Preprint", 
      "type": "publication"
    }, 
    "subjects": [
      {
        "identifier": "11", 
        "scheme": "pmid", 
        "term": "Number Theory"
      }
    ], 
    "title": "Ellipses and hyperbolas of decomposition of even numbers into pairs of prime numbers"
  }, 
  "owners": [
    224
  ], 
  "revision": 2, 
  "stats": {
    "downloads": 0.0, 
    "unique_downloads": 0.0, 
    "unique_views": 0.0, 
    "version_downloads": 0.0, 
    "version_unique_downloads": 0.0, 
    "version_unique_views": 0.0, 
    "version_views": 0.0, 
    "version_volume": 0.0, 
    "views": 0.0, 
    "volume": 0.0
  }, 
  "updated": "2023-07-08T15:01:44.599849+00:00"
}