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Block #2,647,355

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 9:25:50 PM Β· Difficulty 11.7581 Β· 4,184,707 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8e266dab7db76d08ec3d50266bb60b509575a3e48b2a8605cf51bc425f07c8f6
View on Chainz β†—

Height

#2,647,355

Difficulty

11.758123

Transactions

1

Size

199 B

Version

2

Bits

0bc21451

Nonce

91,791,816

Timestamp

5/3/2018, 9:25:50 PM

Confirmations

4,184,707

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

973a69dd0777fb2095a6b6596336427d7ad109048f2cbc9ccf37e36733bd5d80
Transactions (1)
Coinbase973a69dd0777fb…37e36733bd5d80
1 in β†’ 1 out7.2200 XPM109 B
Adqah8zh…1WwoHJ9t
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.

4.298 Γ— 10⁹⁴(95-digit number)
42983579419606674886…32841761892722129119
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
4.298 Γ— 10⁹⁴(95-digit number)
42983579419606674886…32841761892722129119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.298 Γ— 10⁹⁴(95-digit number)
42983579419606674886…32841761892722129121
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
8.596 Γ— 10⁹⁴(95-digit number)
85967158839213349772…65683523785444258239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.596 Γ— 10⁹⁴(95-digit number)
85967158839213349772…65683523785444258241
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
1.719 Γ— 10⁹⁡(96-digit number)
17193431767842669954…31367047570888516479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.719 Γ— 10⁹⁡(96-digit number)
17193431767842669954…31367047570888516481
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
3.438 Γ— 10⁹⁡(96-digit number)
34386863535685339908…62734095141777032959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.438 Γ— 10⁹⁡(96-digit number)
34386863535685339908…62734095141777032961
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
6.877 Γ— 10⁹⁡(96-digit number)
68773727071370679817…25468190283554065919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.877 Γ— 10⁹⁡(96-digit number)
68773727071370679817…25468190283554065921
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
1.375 Γ— 10⁹⁢(97-digit number)
13754745414274135963…50936380567108131839
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:57,900,619 XPMΒ·at block #6,832,061 Β· updates every 60s
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