[QUOTE=3.14159;225193]Oh, wait: This is easy:

3
5
2^3+1 = 9 = 3*3[/QUOTE]

See? You've learned my trick of finding the smallest possible example! :smile:

[QUOTE=3.14159;225193]@CRG: I found this number with the following properties:

49152096000^1+1 is prime. (49152096001)
49152096000^2+1 is prime. (2415928541193216000001)

And: 49152096000^3+1 has n^1+1 as its smallest prime factor:

49152096000^3+1 = 49152096001 * 2415928541144063904001 [/QUOTE]

[code]forprime(p=2,1e4,
k=p*(p-2)+2;
if(isprime(k)&isprime(k-p+1),
print(p," ",k," ",(p-1)^3+1)
)
)[/code]

There are 835 such primes below a million, 4779 below ten million, and 31057 below a hundred million. (I'm referring to the first prime only; the other prime and the composite are of course larger.)

both ^1+1 and ^2+1 seem to have the same digital root.

[QUOTE=science_man_88;225194]my idea is this:

[CODE]#M %9[SUB]1[/SUB] %9[SUB]2[/SUB] %9[SUB]3[/SUB]
2 3 1 4 x
3 3 1 4
5 3 [/CODE]

care to use the data in the table to calculate x ?[/QUOTE]

I don't understand the table. What's x? What's #M? What do the center columns mean?

[QUOTE=science_man_88]both ^1+1 and ^2+1 seem to have the same digital root.
[/QUOTE]

Digital root = Number mod 9.

8 mod 9 = 1.
50 mod 9 = 5.

8=/=5.

Conjecture disproven. The law of small numbers prevails yet again.

Odd counterexample:

30+1 mod 9 = 4.
30^2+1 mod 9 = 1
4 =/= 1

[QUOTE=science_man_88;225196]both ^1+1 and ^2+1 seem to have the same digital root.[/QUOTE]

No, not usually. Run the code I posted to look at small examples -- the first half-dozen all fail.

[QUOTE=3.14159;225198]Digital root = Number mod 9.

8 mod 9 = 8.
8 * 8 mod 9 = 64 mod 9 = 1.

Conjecture disproven. The law of small numbers prevails yet again[/QUOTE]

I think he meant only the numbers that fulfill your conditions rather than just any number. But it's wrong either way.

# m is the amount of Mersenne numbers you multiply together %9 means mod 9 and the subscript is the index in the sequence for that #M .

[QUOTE=3.14159;225198]Digital root = Number mod 9.

8 mod 9 = 1.
50 mod 9 = 5.

8=/=5.

Conjecture disproven. The law of small numbers prevails yet again.

Odd counterexample:

31 mod 9 = 4.
901 mod 9 = 1
4 =/= 1[/QUOTE]

I summed the digits Pi and I got both having a additive root of 1.

[QUOTE=science_man_88]I summed the digits Pi and I got both having a additive root of 1.
[/QUOTE]

Tell me: How did you reduce infinity to 1?

[QUOTE=science_man_88;225200]# m is the amount of Mersenne numbers you multiply together %9 means mod 9 and the subscript is the index in the sequence for that #M .[/QUOTE]

Means nothing to me.

You have three columns for %9 but they have different values. I don't know why and you haven't said.

Are you really multiplying 5 different Mersenne numbers together? That's what you say, but I'd be more inclined to believe 5 as the exponent of the first of two Mersenne numbers you multiply.

And what is the x and what would allow us to find it?

[QUOTE=3.14159;225202]Tell me: How do you know the additive root of infinity?[/QUOTE]

I'm talking [TEX]\sum[/TEX](digits of both) =1

[QUOTE=science_man_88]I'm talking (digits of both) =1
[/QUOTE]

The sum of the digits of pi = 1? So 3.141592653589793238462643383279... = 1? Give us your math proof if this.

For the lulz:

[code]3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955321165344987202755960236480665499119881834797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548161361157352552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383827967976681454100953883786360950680064225125205117392984896084128488626945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645995813390478027590099465764078951269468398352595709825822620522489407726719478268482601476990902640136394437455305068203496252451749399651431429809190659250937221696461515709858387410597885959772975498930161753928468138268683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244136549762780797715691435997700129616089441694868555848406353422072225828488648158456028506016842739452267467678895252138522549954666727823986456596116354886230577456498035593634568174324112515076069479451096596094025228879710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821682998948722658804857564014270477555132379641451523746234364542858444795265867821051141354735739523113427166102135969536231442952484937187110145765403590279934[/code]

The first 2800 digits of pi. Remember, the sum of those digits is 1! LOL!

You do realize that the only number whose sum of digits is 1 is 1, correct?