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Old 2020-02-13, 12:22   #1
tuckerkao
 
Jan 2020

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Default Twin Primes with 128 Decimal Digits

2191*390*82589933*40463441610*232792560±1

Click the attached thumbnail to view all the digits in decimal base.

Would like to know why when the number consists 82,589,933 as the factor will result in twin primes at certain power combinations.
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Last fiddled with by tuckerkao on 2020-02-13 at 12:24
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Old 2020-02-15, 04:06   #2
ewmayer
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@tuckertao: It would help if you explained how you chose/found the above pair, and why you think it is somehow special. You have a large-ish smooth part in form of 2^191*3^90, then the largest-known Mersenne prime exponent, but I see nothing special about the remaining multiplier 40463441610*232792560 = 9419588158802421600. If I define a = 2^191*3^90*82589933, set n to your -prime, then successively increment n by a, I can easily find the next-larger pair of this form,
Code:
n = 21310867332998259383016283883353020788678719772398547918516685244168507150940923363729663389961621332915816701945558484016693248+-1
 = 2^191*3^90*82589933*9419588158802425428+-1 = 2^193*3^91*82589933*11*29*89*27648398432609+-1.
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Old 2020-02-16, 06:23   #3
tuckerkao
 
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Quote:
Originally Posted by ewmayer View Post
@tuckertao: It would help if you explained how you chose/found the above pair, and why you think it is somehow special.]
I chose 2191*390*82589933 because my prime number generator only allowed 128 max digits.

My formula is 2n*3m*prime*large abundant number±1

I'm wondering whether it's still possible to find the next larger pair when both n and m are in the millions or larger with a mega-prime possibly the largest known Mersenne Prime.

I go from 20*3m to 2n*30, so I have a whole Arc rotation on a given orbit(fix # of numerical digits), doesn't have to be 128 digits, it can be 24 millions+ total.

Last fiddled with by tuckerkao on 2020-02-16 at 06:24
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