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Old 2019-04-30, 08:20   #23
robert44444uk
 
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Jun 2003
Oxford, UK

22×3×7×23 Posts
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Some more results:

First instance gaps in consecutive order - everything found up to and including 1878.

Code:
1636	1035211477332	robert44444uk
1637	314387243880	Thomas11
1638	223187612730	Thomas11
1639	430370370398	Thomas11
1640	251399472527	Thomas11
1641	272511992827	Thomas11
1642	212024898078	Thomas11
1643	158850706422	ATH
1644	1201386008933	robert44444uk
1645	464373757405	Thomas11
1646	197557993677	ATH
1647	384183995148	Thomas11
1648	555439323975	Thomas11
1649	158176828393	ATH
1650	409316753062	Thomas11
1651	312158180092	Thomas11
1652	470531332488	Thomas11
1653	841664786197	Thomas11
1654	701771647838	Thomas11
1655	405384059735	Thomas11
1656	514927351307	Thomas11
1657	229220533173	Thomas11
1658	166226961612	ATH
1659	165136905488	ATH
1660	133864375453	ATH
1661	633288781027	Thomas11
1662	256117920503	Thomas11
1663	492030454557	Thomas11
1664	131415761768	ATH
1665	291876048707	Thomas11
1666	802227020182	Thomas11
1667	375860209433	Thomas11
1668	285028014162	Thomas11
1669	859713724753	Thomas11
1670	295839732305	Thomas11
1671	579035340417	Thomas11
1672	161263436148	ATH
1673	498618428432	Thomas11
1674	636283516158	Thomas11
1675	616638723823	Thomas11
1676	859939543782	Thomas11
1677	508171256813	Thomas11
1678	487863089385	Thomas11
1679	600200255728	Thomas11
1680	448760176352	Thomas11
1681	569028734977	Thomas11
1682	280877509220	Thomas11
1683	1019626449685	robert44444uk
1684	435854938013	Thomas11
1685	256321846760	Thomas11
1686	1025620695957	robert44444uk
1687	156290145345	ATH
1688	611197905670	Thomas11
1689	984424116398	Thomas11
1690	652938228583	Thomas11
1691	463542106657	Thomas11
1692	254281560703	Thomas11
1693	431955803822	Thomas11
1694	334135265893	Thomas11
1695	282763122140	Thomas11
1696	450016651352	Thomas11
1697	822643098295	Thomas11
1698	565141146050	Thomas11
1699	372837607753	Thomas11
1700	58917239540	ATH
1701	433407295157	Thomas11
1702	298348323303	Thomas11
1703	466812660410	Thomas11
1704	1045077852373	robert44444uk
1705	517453687215	Thomas11
1706	772867305887	Thomas11
1707	524920422073	Thomas11
1708	459952950865	Thomas11
1709	515336777288	Thomas11
1710	89470349442	ATH
1711	1437737041932	robert44444uk
1712	567801655963	Thomas11
1713	216733386980	Thomas11
1714	1039648289663	robert44444uk
1715	555007406300	Thomas11
1716	485816451332	Thomas11
1717	504463536573	Thomas11
1718	661561148110	Thomas11
1719	325264034063	Thomas11
1720	453489992522	Thomas11
1721	1253001163102	robert44444uk
1722	610655512490	Thomas11
1723	80799633875	ATH
1724	634233966553	Thomas11
1725	762318092370	Thomas11
1726	261705340277	Thomas11
1727	225881516975	Thomas11
1728	538335755667	Thomas11
1729	806506374413	Thomas11
1730	217895151387	Thomas11
1731	707703825092	Thomas11
1732	735596463515	Thomas11
1733	768450016780	Thomas11
1734	745631868578	Thomas11
1735	356177753412	Thomas11
1736	741222736422	Thomas11
1737	761250576468	Thomas11
1738	671721527412	Thomas11
1739	1214363016178	robert44444uk
1740	384364766532	Thomas11
1741	563317414062	Thomas11
1742	724809604908	Thomas11
1743	370979739580	Thomas11
1744	359521940948	Thomas11
1745	300186232845	Thomas11
1746	447197130142	Thomas11
1747	907203956603	Thomas11
1748	528077281142	Thomas11
1749	801659775458	Thomas11
1750	280488680647	Thomas11
1751	739849772267	Thomas11
1752	496386470473	Thomas11
1753	714960674750	Thomas11
1754	338841041033	Thomas11
1755	532001966893	Thomas11
1756	671605907382	Thomas11
1757	294509651840	Thomas11
1758	1278737589385	robert44444uk
1759	298338286438	Thomas11
1760	1175000358333	robert44444uk
1761	584390565997	Thomas11
1762	318182662973	Thomas11
1763	600635385640	Thomas11
1764	240121693893	Thomas11
1765	1204735995605	robert44444uk
1766	473256996777	Thomas11
1767	828485975438	Thomas11
1768	1176057612252	robert44444uk
1769	782711361523	Thomas11
1770	855953593323	Thomas11
1771	988638208437	Thomas11
1772	655550748640	Thomas11
1773	411932055292	Thomas11
1774	447362234533	Thomas11
1775	449770326922	Thomas11
1776	805225566947	Thomas11
1777	550358556340	Thomas11
1778	106405396032	ATH
1779	2129562021213	robert44444uk
1780	982232544190	Thomas11
1781	841171099652	Thomas11
1782	1224262909268	robert44444uk
1783	1422392477865	robert44444uk
1784	1195747448213	robert44444uk
1785	130744752537	ATH
1786	825384984377	Thomas11
1787	776268942683	Thomas11
1788	854615602792	Thomas11
1789	646099785688	Thomas11
1790	557950608758	Thomas11
1791	369489065347	Thomas11
1792	689680764418	Thomas11
1793	1037083894142	robert44444uk
1794	621462178578	Thomas11
1795	750466894258	Thomas11
1796	2175761168042	robert44444uk
1797	582262097498	Thomas11
1798	608219715197	Thomas11
1799	244370452833	Thomas11
1800	831467803302	Thomas11
1801	1052870164587	robert44444uk
1802	800163087448	Thomas11
1803	1306998722697	robert44444uk
1804	1382597845958	robert44444uk
1805	1166113583162	robert44444uk
1806	363596492507	Thomas11
1807	589681107438	Thomas11
1808	374311870175	Thomas11
1809	1519940585608	robert44444uk
1810	133135498198	ATH
1811	754512505717	Thomas11
1812	1225517231188	robert44444uk
1813	1177115829552	robert44444uk
1814	1622632461223	robert44444uk
1815	169866686215	ATH
1816	536707956407	Thomas11
1817	956610710023	Thomas11
1818	707849433580	Thomas11
1819	478026230448	Thomas11
1820	524708956392	Thomas11
1821	1545928373782	robert44444uk
1822	363792713305	Thomas11
1823	393901596172	Thomas11
1824	2530550769183	robert44444uk
1825	718703397508	Thomas11
1826	1197393987332	robert44444uk
1827	514690190788	Thomas11
1828	544205194130	Thomas11
1829	1682087625368	robert44444uk
1830	283716126022	Thomas11
1831	1024442893122	robert44444uk
1832	746075980130	Thomas11
1833	1171018474300	robert44444uk
1834	1461304039818	robert44444uk
1835	1236784093577	robert44444uk
1836	663607308612	Thomas11
1837	361289615670	Thomas11
1838	284106487357	Thomas11
1839	1320327308713	robert44444uk
1840	389453919375	Thomas11
1841	738549390442	Thomas11
1842	1084227409855	robert44444uk
1843	737313907580	Thomas11
1844	1889285158138	robert44444uk
1845	1537365969212	robert44444uk
1846	823245280032	Thomas11
1847	675857800098	Thomas11
1848	723741177537	Thomas11
1849	2371460651248	robert44444uk
1850	804839675663	Thomas11
1851	363074768532	Thomas11
1852	1829464862963	robert44444uk
1853	932204536545	Thomas11
1854	1189288485208	robert44444uk
1855	1174605355802	robert44444uk
1856	1297574083922	robert44444uk
1857	729575524785	Thomas11
1858	1123294853522	robert44444uk
1859	2212559422178	robert44444uk
1860	843314053692	Thomas11
1861	2317063539187	robert44444uk
1862	663487911713	Thomas11
1863	336185917595	Thomas11
1864	1417574651223	robert44444uk
1865	781793275960	Thomas11
1866	892852657037	Thomas11
1867	1444042188138	robert44444uk
1868	1989137103455	robert44444uk
1869	1940989213838	robert44444uk
1870	513194527407	Thomas11
1871	971781746092	Thomas11
1872	447811616018	Thomas11
1873	1348365096302	robert44444uk
1874	750393104603	Thomas11
1875	598433097470	Thomas11
1876	1064530504212	robert44444uk
1877	1040113573768	robert44444uk
1878	1694010994357	robert44444uk
New maximal gap champions

Code:
2406	2184023861542
2492	2406221256378

Last fiddled with by robert44444uk on 2019-04-30 at 08:23
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Old 2019-05-01, 08:33   #24
robert44444uk
 
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Jun 2003
Oxford, UK

111100011002 Posts
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More first instance gaps in consecutive order:
Code:
1878	1694010994357	robert44444uk
1879	2910891145493	robert44444uk
1880	904212211453	Thomas11
1881	781557375732	Thomas11
1882	1375789467133	robert44444uk
1883	1086233157432	robert44444uk
1884	2312441429433	robert44444uk
1885	676152407723	Thomas11
1886	1994026684367	robert44444uk
1887	426285083663	Thomas11
1888	1709285542095	robert44444uk
1889	1739008877393	robert44444uk
1890	151287342070	ATH
1891	1247181224132	robert44444uk
1892	201865544225	Thomas11
1893	290614184492	Thomas11
1894	1666811164798	robert44444uk
1895	854745621275	Thomas11
1896	1747405088257	robert44444uk
1897	359738661993	Thomas11
1898	132437316545	ATH
1899	2043213269438	robert44444uk
1900	619983477157	Thomas11
1901	635700745862	Thomas11
1902	1068189680728	robert44444uk
1903	675525244735	Thomas11
1904	1984692216588	robert44444uk
1905	932239203395	Thomas11
1906	1279486288362	robert44444uk
1907	1202177228578	robert44444uk
1908	1222826404275	robert44444uk
1909	2656430331093	robert44444uk
1910	1551507663815	robert44444uk
1911	1670504219247	robert44444uk
1912	804438922933	Thomas11
1913	2627897440455	robert44444uk
1914	1488017568723	robert44444uk
1915	470420475572	Thomas11
1916	3299752653517	robert44444uk
1917	1165423934903	robert44444uk
1918	804794472115	Thomas11
1919	1572478640448	robert44444uk
1920	2374547901280	robert44444uk
1921	3107951516387	robert44444uk
1922	2554599702130	robert44444uk
1923	1395252802692	robert44444uk
1924	1696444081623	robert44444uk
1925	523274691888	Thomas11
1926	696620005307	Thomas11
1927	2201959145610	robert44444uk
1928	1181669865490	robert44444uk
1929	2034243019588	robert44444uk
1930	1880103150370	robert44444uk
And two new maximal gap champions

Code:
2566	3051148531252
2620	3142272204202
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Old 2019-05-01, 12:20   #25
mart_r
 
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Dec 2008
you know...around...

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Quote:
Originally Posted by robert44444uk View Post
There were 27,412,678 twin prime gaps, of which

8,632,028 were 0 mod5
3,221,541 were 1 mod5
6,415,438 were 2 mod5
6,086,566 were 3 mod5
3,057,104 were 4 mod5

So the 0mod5 case is made.
A small spreadsheet that takes into account prime factors <= 23 and k=1..35 already produces good approximations:
Code:
n mod 5: possibilities/23#  (in  %) approx. actual
0 mod 5: 18772884/223092870 (32.2%) 8814853 8632028
1 mod 5:  6616194/223092870 (11.3%) 3106650 3221541
2 mod 5: 13092786/223092870 (22.4%) 6147750 6415438
3 mod 5: 13438254/223092870 (23.0%) 6309965 6086566
4 mod 5:  6460323/223092870 (11.1%) 3033460 3057104
The mod 7 race looks similarly good:
Code:
n mod 7: possibilities/23#  (in  %) approx. actual
0 mod 7: 11405700/223092870 (19.5%) 5355574 4955717
1 mod 7:  7502625/223092870 (12.9%) 3522876 3481004
2 mod 7:  9173220/223092870 (15.7%) 4307308 4418659
3 mod 7:  6734070/223092870 (11.5%) 3161999 3464620
4 mod 7:  7193970/223092870 (12.3%) 3377946 3288570
5 mod 7:  9431448/223092870 (16.2%) 4428559 4510772
6 mod 7:  6939408/223092870 (11.9%) 3258416 3293335
For mod 11 the bias should also go to 0 mod 11, but a) the bias is less strong and b) for small p, in patterns of the form p+{0,2,11*6*k,11*6*k+2} there is a high probability that the gap is "broken" by a twin prime in-between.

I'd like to work a bit more on the theoretical side, but not today.
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Old 2019-05-02, 12:35   #26
robert44444uk
 
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Jun 2003
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Not many results - had a power cut and lost 18 hours.

More first instance gaps in consecutive order:

Code:
1931	4155631964692	robert44444uk
1932	960136903043	Thomas11
1933	1521234330052	robert44444uk
1934	1368396113168	robert44444uk
1935	664808242868	Thomas11
1936	279967183457	Thomas11
1937	642270715125	Thomas11
1938	1952055775092	robert44444uk
1939	2685610093078	robert44444uk
1940	1435690154763	robert44444uk
1941	1675555446682	robert44444uk
1942	1807383125718	robert44444uk
1943	1042310309512	robert44444uk
1944	1987277275398	robert44444uk
1945	1194795033583	robert44444uk
1946	1267188286017	robert44444uk
1947	1501956317263	robert44444uk
1948	1951682334595	robert44444uk
1949	2200992979138	robert44444uk
1950	982578277387	Thomas11
1951	2593578914117	robert44444uk
1952	3995636455535	robert44444uk
1953	954508482785	Thomas11
1954	2657480397133	robert44444uk
1955	511426336883	Thomas11
1956	1973565186282	robert44444uk
1957	2410733153433	robert44444uk
1958	757895739535	Thomas11
1959	2369918267188	robert44444uk
1960	1603135467927	robert44444uk
1961	2968060543052	robert44444uk
1962	1994746446703	robert44444uk
1963	2935129139030	robert44444uk
1964	1717072682918	robert44444uk
1965	2473396853452	robert44444uk
1966	2093345628637	robert44444uk
1967	2128700932355	robert44444uk
1968	652547157105	Thomas11
1969	1116171078598	robert44444uk
1970	2430451536737	robert44444uk
1971	824751367527	Thomas11
1972	1484101843865	robert44444uk
1973	2352937470705	robert44444uk
1974	3233083864468	robert44444uk
1975	2671923996808	robert44444uk
1976	1629196186112	robert44444uk
1977	1757002494653	robert44444uk
1978	1794428376172	robert44444uk
1979	614991456963	Thomas11
1980	2568440910493	robert44444uk
1981	2948381547562	robert44444uk
1982	1800405738840	robert44444uk
1983	2128859873052	robert44444uk
1984	564720846228	Thomas11
1985	1432632140313	robert44444uk
1986	944675774037	Thomas11
1987	645901356965	Thomas11
1988	1912867539580	robert44444uk
1989	2288073926553	robert44444uk
1990	1178585706107	robert44444uk
1991	1980589742282	robert44444uk
1992	3469535385503	robert44444uk
1993	1333290080990	robert44444uk
1994	721147884418	Thomas11
1995	1081507694722	robert44444uk
1996	3141922816902	robert44444uk
1997	207741061965	Thomas11
1998	2050666865585	robert44444uk
1999	3464628536498	robert44444uk
2000	2023303922073	robert44444uk
2001	4583730314427	robert44444uk
2002	1418099818398	robert44444uk
2003	2752341660315	robert44444uk
2004	3357194177253	robert44444uk
2005	1919394253212	robert44444uk
2006	541952390642	Thomas11
2007	1294793177503	robert44444uk
2008	2804001127870	robert44444uk
2009	3950601685453	robert44444uk
2010	2210130019925	robert44444uk
2011	2454054105092	robert44444uk
2012	1355880364715	robert44444uk
2013	1605983743805	robert44444uk
2014	2416115747078	robert44444uk
2015	1366762534618	robert44444uk
2016	389348710292	Thomas11
2017	2367795362585	robert44444uk
2018	1320531199235	robert44444uk

And two new maximal gap champions

Code:
2727	3879247944150
2737	3939046764478
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Old 2019-05-03, 08:48   #27
robert44444uk
 
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One day later, and I have still not found a 2019 first instance gap or a new champion. Once a 2019 is found, the next few gaps are 2026, 2056, 2076, 2094, 2104 and 2118.

Last fiddled with by robert44444uk on 2019-05-03 at 08:49
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Old 2019-05-03, 15:39   #28
rudy235
 
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Jun 2015
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Quote:
Originally Posted by robert44444uk View Post
One day later, and I have still not found a 2019 first instance gap or a new champion. Once a 2019 is found, the next few gaps are 2026, 2056, 2076, 2094, 2104 and 2118.

Isin't it interesting that it is simpler and easier to find a 2019 gap between TPs than a 1432 (in reality a 716) gap between primes?
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Old 2019-05-03, 16:56   #29
robert44444uk
 
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Quote:
Originally Posted by rudy235 View Post
Isin't it interesting that it is simpler and easier to find a 2019 gap between TPs than a 1432 (in reality a 716) gap between primes?
And here it is

2019 6221183861883
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Old 2019-05-04, 12:57   #30
robert44444uk
 
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Here is a continuation of the consecutive first instance gaps table. The next holes to fill are 2076,2161,2166,2206,2213,2221

Code:
2019	6221183861883	robert44444uk
2020	1110837159180	robert44444uk
2021	3412298008772	robert44444uk
2022	1778401623575	robert44444uk
2023	224142765215	Thomas11
2024	3215430388433	robert44444uk
2025	2125059642060	robert44444uk
2026	7067370983472	robert44444uk
2027	1513315229030	robert44444uk
2028	1693568705267	robert44444uk
2029	548899132323	Thomas11
2030	1159591145647	robert44444uk
2031	1505148947332	robert44444uk
2032	801995327063	Thomas11
2033	2351288605232	robert44444uk
2034	4224109577518	robert44444uk
2035	4026757323885	robert44444uk
2036	3931186336557	robert44444uk
2037	2705967130983	robert44444uk
2038	3387561962360	robert44444uk
2039	1765539534353	robert44444uk
2040	1457630950535	robert44444uk
2041	1883891803437	robert44444uk
2042	1102539778813	robert44444uk
2043	2921284067565	robert44444uk
2044	4053631947823	robert44444uk
2045	1654904607582	robert44444uk
2046	1893143295297	robert44444uk
2047	2044240673680	robert44444uk
2048	249479281077	Thomas11
2049	1749338700963	robert44444uk
2050	2429765299182	robert44444uk
2051	2022886871932	robert44444uk
2052	2237662588513	robert44444uk
2053	1954343550155	robert44444uk
2054	4312142247483	robert44444uk
2055	1736484709050	robert44444uk
2056	6252056887127	robert44444uk
2057	1327506760473	robert44444uk
2058	3083403369492	robert44444uk
2059	2120344096833	robert44444uk
2060	1506078160848	robert44444uk
2061	3876812924082	robert44444uk
2062	2139376161545	robert44444uk
2063	1866827870457	robert44444uk
2064	4398616732228	robert44444uk
2065	2492202785263	robert44444uk
2066	1981415725767	robert44444uk
2067	2551619222068	robert44444uk
2068	1462559617500	robert44444uk
2069	1843167383188	robert44444uk
2070	1042838539733	robert44444uk
2071	5663032539447	robert44444uk
2072	461157712565	Thomas11
2073	902743525100	Thomas11
2074	646834943323	Thomas11
2075	1226421246838	robert44444uk

And 2 new maximal gaps

Code:
2765	6422266971838
2816	7282923065232

Last fiddled with by robert44444uk on 2019-05-04 at 12:58
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Old 2019-05-04, 15:20   #31
Bobby Jacobs
 
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May 2018

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Quote:
Originally Posted by rudy235 View Post
Isin't it interesting that it is simpler and easier to find a 2019 gap between TPs than a 1432 (in reality a 716) gap between primes?
It is interesting that the first missing gap of 2019 is the same as this year.
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Old 2019-05-05, 06:35   #32
robert44444uk
 
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Originally Posted by Bobby Jacobs View Post
It is interesting that the first missing gap of 2019 is the same as this year.
Not if you are a Buddhist. They are waiting with breath held in anticipation for the first gap of 2562.

Muslims are no doubt already digesting that 34516209527 is the first instance gap of length 1440, and are seriously considering an award to ATH as its discoverer.

In my previous domicile in Bangladesh, 1426 is the year, 114261540757 is the gap, and ATH is again the hero.

I will no doubt get plaudits in Ethiopia for my discovery of a size 2011 gap 2454054105092

We may even in time get to 5779, where it is in the Hebrew calendar, although by the time we get there it might be 5880.

So to answer your question, no, its not terribly interesting

Last fiddled with by robert44444uk on 2019-05-05 at 06:35
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Old 2019-05-05, 15:57   #33
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Originally Posted by robert44444uk View Post
Not if you are …

So to answer your question, no, its not terribly interesting

Well said!


But you did forget the Mayans
Ohh this occidentalists! When will we get a gap of 5133?
Perhaps it will be on the year 5134?
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