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Block #42,320

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 6:23:24 PM Β· Difficulty 8.5926 Β· 6,763,734 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
96c6cc81f9efc227b85c7c207e009093a437ce3857c74c69be0a17c4dc9cca75
View on Chainz β†—

Height

#42,320

Difficulty

8.592568

Transactions

1

Size

204 B

Version

2

Bits

0897b284

Nonce

1,494

Timestamp

7/14/2013, 6:23:24 PM

Confirmations

6,763,734

Mined by

⛏️ P2SHAXWphP8TebwduDiYciZuMF4H344trwmtBM

Merkle Root

cae23d384cd26c38cf4c907460a84449865db4d8d343277e36566864861dea9f
Transactions (1)
Coinbasecae23d384cd26c…566864861dea9f
1 in β†’ 1 out13.5300 XPM110 B
AXWphP8T…4trwmtBM
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.

3.844 Γ— 10¹⁰⁡(106-digit number)
38440057931521457056…00892685331341303519
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
3.844 Γ— 10¹⁰⁡(106-digit number)
38440057931521457056…00892685331341303519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.844 Γ— 10¹⁰⁡(106-digit number)
38440057931521457056…00892685331341303521
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
7.688 Γ— 10¹⁰⁡(106-digit number)
76880115863042914113…01785370662682607039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.688 Γ— 10¹⁰⁡(106-digit number)
76880115863042914113…01785370662682607041
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
1.537 Γ— 10¹⁰⁢(107-digit number)
15376023172608582822…03570741325365214079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.537 Γ— 10¹⁰⁢(107-digit number)
15376023172608582822…03570741325365214081
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
3.075 Γ— 10¹⁰⁢(107-digit number)
30752046345217165645…07141482650730428159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.075 Γ— 10¹⁰⁢(107-digit number)
30752046345217165645…07141482650730428161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,692,515 XPMΒ·at block #6,806,053 Β· updates every 60s
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