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Forum: enzocreti 2020-07-23, 07:33
Replies: 0
Views: 73
Posted By enzocreti
pg(308899)

pg(69660) is prime
pg(92020) is prime and 92020+239239 is prime
pg(92020+239239) is prime




Now i consider
Forum: enzocreti 2020-07-02, 09:29
Replies: 0
Views: 117
Posted By enzocreti
collatz 3x+1

I found a forumula about the 3x+1 problem


let be T(k,n) the trajectory starting from integer n.


k is the number of iterations


T(0,n)=n i think
Forum: enzocreti 2020-06-21, 22:01
Replies: 4
Views: 865
Posted By enzocreti
Pg(69660) pg(92020) and pg(541456) pg(k) primes with k multiple of 86

This identity involves pg(k) primes with k multiple of 86

k multiple of 86 with pg(k) primes satisfy this identity

541456-(69660*16/10+1000)=1000*sqrt(92020*2+1)


pg(366770) is prime and...
Forum: enzocreti 2020-06-20, 17:55
Replies: 4
Views: 865
Posted By enzocreti
Pg(6231) and pg(51456)

There are two primes pg(6231) and pg(51456) with 6231 and 51456 multiple of 201

51456(even)=201*(2^8)
6231(odd)=201*(2^5-1)

Pg(541456) is probab prime

541456=(46^2-1)*2^8+2^4
Forum: enzocreti 2020-06-19, 21:12
Replies: 0
Views: 149
Posted By enzocreti
Lcm(344,559) 331 and pg primes

Pg(215), pg(69660),pg(92020) pg(541456) are prp with 215, 69660, 92020 and 541456 multiple of 43.

215, 69660, 92020, 541456 are plus/minus 344 mod 559

lcm(344,559)=4472

4472=8*331+456*4
...
Forum: enzocreti 2020-06-18, 19:26
Replies: 4
Views: 865
Posted By enzocreti
Pg(92020) and pg(331259)

Pg(92020) and pg(331259) are probable primes

331259=92020+239239

92020 and 331259 are congruent to 5 mod ((331+456*6)*6+1) where 3067=331+456*6 is a prime
Forum: enzocreti 2020-06-17, 10:45
Replies: 4
Views: 865
Posted By enzocreti
Pg(92020) pg(69660) and pg(541456)

Pg(92020) pg(69660) and pg(541456) are primes
92020 541456 69660 are 10^m mod 41 and multiple of 43

541456 is multiple of 787

92020 and 69660 are congruent to 10^s mod (787+456*r) for some...
Forum: enzocreti 2020-06-15, 10:24
Replies: 4
Views: 865
Posted By enzocreti
Smile Pg(75894) and pg(56238) and other random pg(x)

Pg(75894) and pg(56238) are primes or at least probable primes

I noticed that 75894 and 56248 are multiple of 546 and congruent to 24 mod 54

Using Wolphram (Chinese remainder theorem) I was...
Forum: enzocreti 2020-06-14, 08:04
Replies: 2
512
Views: 163
Posted By enzocreti
512

Is 512 the only cube with the property that if the digits are reversed, the reverse 215 is a cube minus one?
Forum: enzocreti 2020-06-13, 11:59
Replies: 0
Views: 117
Posted By enzocreti
3 classes of pg primes

I noticed that there are at least 3 pg(k) primes with k multiple of something

I mean

Pg(215), pg(69660), pg(92020) with 215, 69660, 92020 multiple of 215

pg(6231) and pg(51456) with 6231 and...
Forum: enzocreti 2020-06-13, 10:14
Replies: 0
Views: 127
Posted By enzocreti
Infinitely many of such primes?

pg(75894) and pg(56238) are probable primes

75894 and 56238 are multiple of 546=(1456*3/8)

So the impossible conjecture is:

Are there infinitely many pg(546s) which are primes?
Forum: enzocreti 2020-06-11, 12:44
Replies: 0
Views: 158
Posted By enzocreti
why this happens?

Here a list of primes congruent to 456 mod 559 and to 1 mod 125:


3251
841751
1959751
2379001
3357251
5313751
5453501
Forum: enzocreti 2020-06-10, 18:18
Replies: 1
Views: 288
Posted By enzocreti
Curious fact

(559*5+456) *344=1118344


1118=559*2
And 1118344 is the concatenation in base ten of 1118 and 344

The prime 3251 has this property:

3251*86=279586...2795 is a multiple of 559 and 279586 is...
Forum: enzocreti 2020-06-10, 17:23
Replies: 1
Views: 288
Posted By enzocreti
An algebraic trick

(456+559*2) *344=541456.

541456 is congruent to 344 mod 559 and pg(541456) is prime!
Forum: enzocreti 2020-05-10, 15:29
Replies: 0
Views: 669
Posted By enzocreti
Ec prime exponents

Ec primes are primes formed by concatenation in base 10 of two consecutive Mersenne numbers, 157 for example.


The form is

(2^k-1)*10^d + 2^(k-1)-1=P(k) where d is the number of decimal digits...
Forum: enzocreti 2020-04-04, 11:47
Replies: 0
Views: 438
Posted By enzocreti
Is this fact provable?

I asked it on mathexchange but I did not receive a clear answer.


Consider this Pari code:

liste(lim,mul,base=34,step=5590,offset=588)=my(v=List(),X=mul*base); lim\=1;...
Forum: enzocreti 2020-03-30, 23:06
Replies: 7
Views: 1,287
Posted By enzocreti
... I note also...

I note also that


(lcm(215,344,559))^2=4999*10^5+69660-60


I note that the polynomial

X^2-X*429^2+7967780460=0 has the solution x=69660
Forum: enzocreti 2020-03-30, 17:39
Replies: 7
Views: 1,287
Posted By enzocreti
http://factordb.com/index.php?id=11000000011108011...

http://factordb.com/index.php?id=1100000001110801143

http://factordb.com/index.php?query=%282%5E92020-1%29*10%5E27701%2B2%5E92019-1
Forum: enzocreti 2020-03-30, 12:50
Replies: 7
Views: 1,287
Posted By enzocreti
...

Well...
actually they are only probable primes... maybe in future they will be proven primes
Forum: enzocreti 2020-03-30, 11:52
Replies: 7
Views: 1,287
Posted By enzocreti
69660 and 92020

69660 and 92020 are multiple of 215 and congruent to 344 mod 559
92020=lcm(215,344,559)+69660


| denotes concatenation in base 10


2^69660-1 | 2^69559-1 is prime
2^92020-1 | 2^92019-1 is...
Forum: enzocreti 2020-03-21, 21:54
Replies: 6
Views: 834
Posted By enzocreti
How to proof it?

How to proof it?
Forum: enzocreti 2020-03-21, 21:47
Replies: 6
Views: 834
Posted By enzocreti
Diophantine equation

Are there infinitely many solutions to these Diophantine equation


10^n-a^3-b^3=c^2 with n, a, b, c positive integers?
Forum: enzocreti 2020-03-20, 14:35
Replies: 3
Views: 500
Posted By enzocreti
216 is the only cube that can be written in this way?

216=3^2*(182^2-331*10^2)


is there any other positive cube that can be written as


a^2*(b^2-r*10^2)?


with a and b positive and coprime, r prime?
Forum: enzocreti 2020-03-20, 10:23
Replies: 1
Views: 505
Posted By enzocreti
31*10^2-13

Consider the example


(31*10^2-13)/9=7^3




are there other primes p and q (with p the reverse of q) besides 31 and 13, such that
Forum: enzocreti 2020-03-09, 14:46
Replies: 0
Views: 562
Posted By enzocreti
3-variable function

let be



f(x,y,z)=344x+22919y+215z




I search integers k such that
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