What's new

July 22, 2009

• Daniel Morel announced a solution of Chapter 11 : aⁿ≡c (mod n).
  for a=3 and c=56, n=50369033879 is the smallest solution.
  I also found the solutions for a=3, c=14, 34 and a=7, c=36 are listed in
  The On-Line Encyclopedia of Integer Sequences.

April 01, 2009

• Richard Fischer is computing Chapter 11 : Wieferich prime.
  Under 2.31 x 10¹² were cheched by him.

December 01, 2008

• Appendix 5 : Prime table was updated.
  This page shows the following interesting prime tables,
  
  
  1. n-bit prime (primes near to 2ⁿ : 1 ≤ n ≤ 3100)
  2. primes near to 10ⁿ (1 ≤ n ≤ 1000)
  3. primes near to n! (factorial : 1 ≤ n ≤ 400)
  4. primes near to #Pn (primorial : 1 ≤ n ≤ 300)
  5. primes near to #Comp_n (compositorial : 1 ≤ n ≤ 550).
  
  "n-bit prime" and "primes near to 10ⁿ" show the first and last ten primes near to these bases.
  "primes near to factorial, primorial and compositorial" show the first and last primes.
  

October 31, 2008

• Chapter 2 : Squares consisted of 3 different digits
  searched for all upto 034, 10^24 and found new sporadic solution,

  44949994999999949999995²= 2020502050500020505000050500052500000500000025 (October 31, 2008)
  20832739723817975138362²= 434003044400343443044430000434430333044043044 (October 31, 2008)
  

August 03, 2008

• Chapter 2 : Squares consisted of 3 different digits
  The search for pattern 013 reached upto 10²⁴, but still there is no solution.

June 22, 2008

• Richard Fischer is computing Chapter 11 : Wieferich prime.
  Under 1.72 x 10¹² were cheched by him.

June 17, 2008

• Richard Fischer announced errata of Chapter 11 : Wieferich prime that
  

  a=919 p=9411713 is false
  a=819 p=9411713 is o.k.
  a=947 p=4204968197 is false
  a=974 p=4204968197 is missing
  a=115 p=2743780307 is missing
  a=148 p=2805469039 is missing
  a=297 p=2779225651 is missing
  a=413 p=2832308863 is missing
  a=723 p=2938943531 is missing
  a=799 p=2891032049 is missing
  a=832 p=112246723 is double
  a=844 p=2816027947 is missing
  

  Thank you very much.

June 09, 2008

• Chapter 2 : Squares consisted of 3 different digits
  New sporadic solution,

  3015775265159011230138²= 9094900449944904494440090444449999999499044 (June 09, 2008)
  

June 02, 2008

• Chapter 2 : Squares consisted of 3 different digits
  Two new sporadic solution,

  3180252254777039538502²= 10114004404014444004140001011411401140404004 (April 28, 2008)
  6674983479713230005962²= 44555404454444540454555540045000554555545444 (June 02, 2008)
  

April 16, 2008

• Chapter 5 : Repeating Decimals were translated in English.
• Chapter 2 : Squares consisted of 3 different digits
  The search range for the solution which contains "0" reached a≤10²¹.
  Only two new sporadic solution were found.

  150167406766664999985²= 22550250055025025225250200022000050000225 (April 07, 2008)
  149067065510873088673²= 22220990020022929092929022220290920900929 (April 07, 2008)
  

April 12, 2008

• Chapter 7 : Collatz's Conjecture [E16]
  and
  Chapter 8 : Continued Fraction and Pell's Equation
  were translated in English.

April 09, 2008

• All the contents of Chapter 3 : n=(x+y+z)(1/x+1/y+1/z) were updated.

April 03, 2008

• Chapter 5 : Repeating Decimals, Remarkable patterns were uploaded.

March 31, 2008

• Started computation of Chapter 2 : Squares consisted of 3 different digits for the solution which contains "0" up to a≤10²¹.

March 24, 2008

• The search range of a^n=c mod n reached up to 10¹⁰ for all data from a=2 to 97.

March 17, 2008

• The search range of a^n=c mod n reached up to 10¹⁰ for a=37 .. 79.

March 02, 2008

• The search range of a^n=c mod n reached up to 10¹⁰ for a=2 .. 31.

February 25, 2008

• The search range of amicable numbers reached up to 10¹⁰.

February 06, 07, 2008

• English version for all chapters' front pages were uploaded.

February 05, 2008

• Chapter 3 n = (x + y + z)(1/x + 1/y + 1/z)
Solutions obtained with Cremona's mwrank are uploaded.

Solutions -500 ≦ n ≦ -1
Solutions 1 ≦ n ≦ 500

February 02, 2008

• The search range of amicable numbers reached up to 5*10⁹.

January 28, 2008

• Front page refined.
• The search range of amicable numbers was extended up to 10⁹.
• aⁿ≡c (mod n) uploaded.

January 21, 2008

• Chapter 11 : Wieferich prime was updated.

December 10, 2007

• Chapter 4 solutions for n=x³+y³+z³ where n=156, 318, 366, 420, 564, 758, 789, 894, 933, 948 were added.

April 19, 2007

• Chapter 4 Leonid Durman announced the new results for n = x³ + y³ + z³.

May 17, 2004

• Chapter 2 : Search range for patterns not including zero were extended up to 10²⁵.
  (For patterns including zero, up to 10²⁰ were serached.)

June 04, 2001

• In Chapter 7, new results by Tomas Oliveira and Silva.
  Their web site is here ( 3x+1 conjecture verification results).

June 22, 2001

• Chapter 6 : Helmut Postl found larger number 10000000525586206 (232 times).

June 04, 2001

• Chapter 7 : Collatz's Conjecture
  Tomas Oliveira and Silva's web site.
  3x+1 conjecture verification results).