# Manfred Toplic

Klagenfurt, Austria

Eastern Longitude: 14° 19' 03"

Northern Latitude: 46° 36' 50"

440 meters ASL

# Astronomy and Mathematics

#### I am a amateur number theorist and amateur astronomer and member of the Astronomical Society of Carinthia

**And here is a page of one of my other hobbies: Oldtimer cars**

## My discovery of

__NINE AND TEN CONSECUTIVE PRIMES IN ARITHMETIC PROGRESSION__

(The amazing Story of the Discovery of Nine and finally Ten CP in AP)

### With Yves Gallot 's program Proth.exe (named after Francois Proth ) I was searching for

Proth Primes (Primes of the form: k * 2^{n} + 1),

Woodall Primes (Primes of the form: n * 2^{n} - 1 )

and for Generalized Fermat Primes (Primes of the form: b^{N} + 1 , with b even and N=2^{n}).

### The largest Proth Prime (with k = 5) I found was

## 5*2^1320487 + 1 (397507 digits)

### At the time of the discovery (March 15, 2002) this was the largest known Proth-Prime and the 7th largest known prime.

## Other large Proth Primes I found:

## 5*2^1282755 + 1 (386148 digits)

## 5*2^819739 + 1 (246766 digits)

###

### At the time of the discovery (September 25, 2000) this was the largest known Woodall Prime:

## 667071*2^667071 - 1 (200815 digits)

### References:

####

### On 1999 April, 23

### have been found.

### (Here I was a member of the search team.)

####

### On 1999 September, 28

### have been found.

#### (A sequence of seven Pythagorean triangles, where

(i) the lengths of the hypotenuse and one leg of each triangle are primes,

and

(ii) the hypotenuse is the shorter leg of the next triangle in the chain.)

### (Here I was also a member of the search team.)

###

### With Tony Forbes program MFAC.EXE I was searching for a factor of MM61, the

###

### Some years ago I participated in Paul Zimmermann' s ECMNET

#### I tried to factorize some of the so-called Cunningham composites with ECM (Elliptic curve method).

###

###

## There are lots of unused (idle) cpu cycles to spare,

and I'm investing them in science !

###

**Last updated on 2021 May 27, by ***Manfred Toplic*