Koen's Korner

Hypotenuses of Primitive Pythagorean Triples Primes – Update #1

bryan — Mon, 17 Oct 2011 17:05:41 +0000

I have completed searching through n-values < 100,000 and here are the results:

9161

2, 10, 50, 58, 70, 118, 150, 222, 250, 262, 758, 1322, 1682, 2050, 5490, 80962, 86262

942 061

1, 7, 17, 37, 71, 217, 227, 337, 1907, 2177, 3383, 3581, 4411, 17747, 29233, 35293, 65203

1 222 141

10, 102, 126, 538, 798, 73950

2 156 041

5, 21, 33, 49, 55, 71, 101, 131, 143, 263, 265, 313, 355, 463, 695, 849, 871, 1605, 2265, 2371, 3039, 3111, 3221, 4609, 6021, 6333, 6679, 7511, 7799, 8731, 9925, 17413, 27361, 31351, 32271, 36931, 47711, 78971, 79701, 87351

88 589 101

41, 89, 97, 127, 167, 229, 317, 377, 527, 629, 657, 1097, 1185, 1549, 1629, 2069, 2329, 2961, 5059, 5457, 5741, 6609, 9117, 9439, 10029, 16591, 29401, 33689, 43247, 62677, 64961, 75619, 85291, 88931, 98257

131 991 001

63, 199, 343, 357, 919, 5373, 8311, 33723, 39973, 55221

198 901 779 305

40, 52, 90, 96, 556, 688, 936, 1450, 1710, 1792, 1816, 2030, 2446, 2890, 4100, 6332, 7070, 9692, 9836, 9976, 13972, 15566, 21886, 22336, 34468, 57506, 84902

184 105 084 021 037

18, 120, 186, 200, 356, 396, 488, 596, 3896, 10440, 10580, 11106, 22040, 32436

385 524 870 425 705

18, 48, 106, 132, 188, 812, 9076, 10140, 13220, 28824, 55840, 72178, 93136, 94000

6 098 542 411 938 841

15, 69, 89, 129, 815, 1269, 1421, 1455, 1529, 1551, 2709, 6521, 10221, 12351, 15855, 32391, 51197, 82841

30 913 065 236 666 477

2, 60, 98, 104, 194, 248, 464, 642, 738, 866, 1122, 1538, 1604, 1746, 2418, 2844, 6830, 9396, 14148, 15374, 27488, 38492, 53088, 54176, 57824, 58188, 65658, 70022, 81312, 99350

32 236 231 327 801 693

11, 123, 155, 227, 415, 543, 835, 8511283, 1403, 2999, 3259, 3475, 4715, 5343, 7019, 7187, 10111, 11251, 13371, 41459, 62871, 64435

184 672 513 372 600 885

51, 97, 145, 219, 595, 1141, 10915, 18075, 25681, 28699, 30265, 46777

467 376 886 819 741 065

3, 7, 23, 31, 39, 43, 79, 91, 457, 491, 617, 163, 241, 379, 2703, 10529, 14723, 16795, 18055, 18331, 23961, 62307, 64203, 75345, 81961

619 813 168 864 541 257

5, 161, 869 2357, 6569, 17477, 28553

New Prime Number Project

bryan — Thu, 13 Oct 2011 18:41:13 +0000

I have long had an interest in prime numbers and utilizing my CPUs for searching for primes. Over the years, I have found 9 primes which have been on Chris Caldwell’s Prime Pages. My results are here.

I am embarking on a new project to locate both Riesel and Proth Primes. Riesel primes are numbers in the form of k*2^n-1 and Proths are those of the form k*2^n+1. The k values that I will be searching are those of the Hypotenuses of Primitive Pythagorean Triples (OEIS:A195502).

The following work has been done so far:

Riesel Primes

k=5: Searched for n’s up to 3,066,000 & 3,499,000 – 3,646,000 with 43 primes found. To help complete the gap, see the post at the Mersenne Forum.

k=397: Searched for n’s up to 1,200,000 with 18 primes found.

k=533: Searched for n’s up to 1,000,000 with 31 primes found.

k=9161: Searched for n’s up to 10,000 with 15 primes found.

The remaining 14 k’s have not been searched.

Proth Primes

k=5: Searched for n’s through 5,660,000 with 25 primes found.

k=397: Searched for n’s through 920,000 with 37 primes found.

k=533: Searched for n’s through 920,000 with 18 primes found.

k=9161: Searched for n’s through 200,000 with 12 primes found.

There is no evidence of any of the other k’s being searched for Proth primes.

Initial thoughts and strategy

Start with the Riesel primes to search all n’s through 1,000,000.
Primes large enough to make the Prime Pages occur once n>666000.
Use sieving tools from Geoffrey Reynolds (srsieve, sr1sieve, sr2sieve).
Worry about the Proth’s later.
Ultimate goal is to search all n’s < 3,000,000 for both Riesel and Proth primes.

Tweets in the past week – 2010-01-24

bryan — Sun, 24 Jan 2010 21:20:00 +0000

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Tweets in the past week – 2009-12-13

bryan — Sun, 13 Dec 2009 13:20:00 +0000

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Tweets in the past week – 2009-12-06

bryan — Sun, 06 Dec 2009 13:20:00 +0000

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Tweets in the past week – 2009-11-29

bryan — Sun, 29 Nov 2009 13:20:00 +0000

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Tweets in the past week – 2009-11-08

bryan — Sun, 08 Nov 2009 13:20:00 +0000

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Research Recap for the Week of 31 Oct 2009, part 1

bryan — Mon, 02 Nov 2009 16:36:51 +0000

Well, better late than never. After a busy weekend with Halloween and the kids, I find myself writing this on Monday morning.

I have updated the data at over on the Koen Family Genealogy site to include all recent discoveries, including those given here.

This week’s activities included a trip to the St. Louis County Library to investigate what they have on Montgomery County, Missouri. In particular there was one book that I wanted to look at, “Family Maps of Montgomery County, Missouri” by Gregory A. Boyd, J.D. Mr. Boyd has taken and mapped out all of the original Federal land grants with in the Montgomery County and others across the country. Unfortunately, I think my research in Montgomery County has taken me far enough back in time to really make use of the book. I am fairly certain that I don’t have all of my direct line ancestors from Montgomery County identified. This should prove to be a very useful book, when I am ready for it.

Building on what I worked on the previous week, I looked at all of the other children of Edward Lee Allen . These would be George Draper Allen (1892-?) and Joseph Burnace Allen (1893-1956) .

What I know about George Draper Allen

According to his WW I Draft Registration Card, he was born 4 Mar 1892 in New Florence, Montgomery, Missouri, USA. He married Bertha J. Ekey on 10 Oct 1914 presumably in Montgomery County, Missouri, USA. At this point, I do not know when he left this world, There is no record in the Missouri Digital Heritage database. I have found him in each of the Federal Censuses from 1900-1930, all in Montgomery County.

I have not done much research on the Ekey family, so what I have for Bertha J. Ekey, is scant. She was born about Aug. 1892, probably in Montgomery County, Missouri, as this is where her siblings were born.

George and Bertha had two daughters:

Jewel E. Allen, b. Abt. 1914.
Vaurine Allen, b. Abt 1917.

Research to do

Determine George Draper Allen’s date of death
Land Records
Newspapers to flesh out other details of his life

Notes

My mother has put me in contact with one of Jewel’s children, who may have some of the data needed on this family as well as the Joseph Burnace Allen family.

There were brothers and sisters who married brothers and sisters, between the Ekey and Allen family. This created double cousins. My maternal grandmother used to talk about this.

Tweets in the past week – 2009-11-01

bryan — Sun, 01 Nov 2009 13:20:00 +0000

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Obituary for Magnolia Elrod Allen (1867-1952)

bryan — Wed, 28 Oct 2009 19:43:52 +0000

From the Montgomery City Standard, 20 Oct 1952, page 1 column 3:

Mrs. E. L. Allen Dies In Wellsville

Magnolia Elrod, daughter of the late James and Amanda Elrod, was bord July 16, 1867 south of Danville, Missouri and departed this life September 25, 1952 in Wellsville, Missouri at the Knight Nursing Home, at the age of 85 years 2 months and 9 days.

At an early age she professed faith in her Savior and united with the Methodist Church. She was a faithful member and, as long as her health permitted, was a regular attendant at Sunday School and church.

On June 9, 1889, she was united in Holy Matriomony in the Methodist Church in Danville with Edward Lee Allen who preceded her in death March 12, 1949. To this union were born four children: Orpha (Mrs. Henry Ekey), George and Burnace all of New Florence, and Frank, who preceded her in death at the tender age of two years.

She leaves to mourn her passing three children, four grandchildren, four great grandchildren; one brother, James Elrod of New Florence; two nieces: Lucy Elrod and Mrs. Helen Groteweil; one nephew, Merlin Elrod; one sister-in-law, Mrs. Jennie Marlow, and many other relatives and a host of friends.

Funeral services were conducted at New Florence Methodist Church Sunday afternoon by her pastor, Rev. Jon Kirk and burial was in New Florence Cemetery—Hopkins service.