20101029, 18:48  #1 
May 2010
Prime hunting commission.
11010010000_{2} Posts 
Prime posting thread, part 2. (With a catch.)
Again, post many, many primes.
But, this time: 1. At least 200 digits. 2. Composed of only two or three numbers. 3. PRPs accepted, although proof is recommended. Let me kick things off.. Code:
99494999494944444449994494999444999999449499999449949944999949999994994944499944949949449494444994994994944449999999994999949449449999994494944994499994494499999994444949994999449494949944444999949949999499999999994494999499449949 And; Code:
49999999999494949194499149994411991449199494194944991994199999444949141494994499949944919949199919119444999449194944991494144994999494994444149499499944991444494944444919194449949994949449491114499941444999119994919419449999919919494994194999419944114499999941199994494491499994911449149491919499149449119994994949914994991999944194994919144991419499444449994441141944919994999149114994914999419999944494499414449141941994499144991491499999194994119491199194194999914441499444999419494149444491949991419449449144494199444419994944944991994944491191494994144999919919999999949194149414949449449499949441491199499914449494919494999991194191944999994199 Or, rather, are both PRP. Last fiddled with by 3.14159 on 20101029 at 18:55 
20101029, 18:57  #2 
May 2010
Prime hunting commission.
11010010000_{2} Posts 
Code:
6666677676677766767666667776767676666666677767767777776667776776666667767767666666767667767766776676677677777676767767776677776766777777767766767777677676677766666766767676667666677777766766776766676767777667777767777767676776766667777766777666676677 Code:
9999995999995599999599999595959999999999959995959959959999999999599959995959599559999999999599999995559999999959995999999595955995999995995999999595559999999555999999999595559595959999959999999999559959999999999999595995559995999999959999999999999959 Code:
599999959555559999595559555999995959955999955999995999995959955555599599995955599959999995999959959999999999955595999599995999995599599959999555959559955559959559995959999959959595599995999595555955959955999955995999999999995995995595595959995999995595999999555599995595999959995995999995995559959995995599955955955995959999999995995999959599999999959999959995555999595959995959599999959955999959995555959999999959595959999959595959555995559999999959 Last fiddled with by 3.14159 on 20101029 at 19:03 
20101029, 22:02  #3 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×3×1,571 Posts 
(10^{12891}+11)/3 has all 3s and a 7 in the end. 12891 digits; tricky to prove (if not for some luck...)  because of the denominator. Just so that it doesn't get lost in that other thread. This one is proven just recently.
A good list of such primes and PRPs is here and here  it is somewhat important to know the existing records, right? A yardstick? (Like in the 'Battle of sexes' thread, in order to beat women's world record it would be a good idea to first find out how much is it exactly.) 
20101030, 00:47  #4 
Aug 2006
3^{2}·5·7·19 Posts 
Well, in the usual spirit of my contributions, I give you
10^{199} + 91119 which is the smallest possible entry. The corresponding smallest with only two distinct decimal digits is 10^{199} + 1110101011. Both of these are, of course, P200s. If I was to cheat and use binary, it would be 2^{199} + 101 = Code:
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001100101_{2} Last fiddled with by CRGreathouse on 20101030 at 00:50 
20101031, 21:15  #5 
May 2010
Prime hunting commission.
11010010000_{2} Posts 
By the way, is there a prime of this type, such that no smaller substring of it is ever prime?
If so, which is the largest for which that's true? Last fiddled with by 3.14159 on 20101031 at 22:00 
20101031, 21:41  #6  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×3×1,571 Posts 
Quote:
E.g. 999999999*10^1802301 doesn't satisfy: substring 89 is prime. Similarly a 4plus9ers will fail with 499 substrings... 1plus0ers stand a good chance, if they stay clear of 11 substrings. Interesting... 

20101031, 21:59  #7 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
10^616+1001001 and 10^668+1001001 match the criteria. 1001 and 1001001 are composite, as are the leading 100...001 and 100...001001 for each number. They're PRPs right now, but I'm proving them.
http://factordb.com/index.php?id=1100000000225031459 (Edit: proven prime by the DB) http://factordb.com/index.php?id=1100000000225031635 (Edit 2: proven prime by me, proof attached; Edit 3: and by the DB) Last fiddled with by MiniGeek on 20101031 at 22:06 
20101101, 00:21  #8 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10010011010010_{2} Posts 
10^n+k with k that spells three 1's and the rest 0's is a good ticket.
This is because substrings of it will have 0,1,2,3 or 4 1's (the last one is itself). However substrings with zero, one and three 1's are easily dismissed (the latter is divisible by 3). So all one needs for the number to belong in the class is to show compositeness of substrings with two 1's, which is not hard. When n is large, these will remain PRPs. k*10^n+1 are even better because they will be proven primes! 
20101101, 00:32  #9  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
Quote:
Code:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 any number or group that has any of the digits:2,3,5,7 any number or group that has any of the sets(2):1'1,1'4(if taken out of that order = 41),1'6(if taken out of that order = 61),1'9,8'9, etc. any way 

20101101, 00:34  #10  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
Quote:


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