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Block #2,641,128

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/1/2018, 6:07:53 AM Β· Difficulty 11.6081 Β· 4,200,952 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
ecdf7e4b3755327affe1bb852b28b96cfe147fce690dc9493b7500c03a4dee56
View on Chainz β†—

Height

#2,641,128

Difficulty

11.608098

Transactions

1

Size

199 B

Version

2

Bits

0b9bac48

Nonce

109,963,851

Timestamp

5/1/2018, 6:07:53 AM

Confirmations

4,200,952

Mined by

⛏️ P2SHAe8T3UQr9kWTaMos2TYPNeGURKg6R86iZC

Merkle Root

bb9eb3d3c4c9032a0bab2c1fd916536b2790664f2815d4d7ed91988b29852ceb
Transactions (1)
Coinbasebb9eb3d3c4c903…91988b29852ceb
1 in β†’ 1 out7.4100 XPM110 B
Ae8T3UQr…g6R86iZC
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.119 Γ— 10⁹²(93-digit number)
41198594935972429933…84259715768291738319
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
4.119 Γ— 10⁹²(93-digit number)
41198594935972429933…84259715768291738319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.119 Γ— 10⁹²(93-digit number)
41198594935972429933…84259715768291738321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
8.239 Γ— 10⁹²(93-digit number)
82397189871944859866…68519431536583476639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.239 Γ— 10⁹²(93-digit number)
82397189871944859866…68519431536583476641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.647 Γ— 10⁹³(94-digit number)
16479437974388971973…37038863073166953279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.647 Γ— 10⁹³(94-digit number)
16479437974388971973…37038863073166953281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
3.295 Γ— 10⁹³(94-digit number)
32958875948777943946…74077726146333906559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.295 Γ— 10⁹³(94-digit number)
32958875948777943946…74077726146333906561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
6.591 Γ— 10⁹³(94-digit number)
65917751897555887893…48155452292667813119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.591 Γ— 10⁹³(94-digit number)
65917751897555887893…48155452292667813121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.318 Γ— 10⁹⁴(95-digit number)
13183550379511177578…96310904585335626239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,981,024 XPMΒ·at block #6,842,079 Β· updates every 60s
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