Block #7,692

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/10/2013, 11:24:36 AM · Difficulty 7.5298 · 6,795,976 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e8118520ec2bb87897faab920ede4e9626d66c5fd1a666955f720c8a94029546

View on Chainz ↗

Height

#7,692

Difficulty

7.529807

Transactions

Size

959 B

Version

Bits

0787a168

Nonce

139

Timestamp

7/10/2013, 11:24:36 AM

Confirmations

6,795,976

Mined by

⛏️ P2SHAUrWxpHq2HjR65G6go5hP1ccuQGSAsrBVi

Merkle Root

fa5b2004c7d3070482abac3e385eacdae598cca5f0f732c0fa5c42c2da5bde65

Transactions (3)

Coinbase9ed8bca1899456…3e81697883eff2

1 in → 1 out17.6300 XPM108 B

AUrWxpHq…GSAsrBVi

6dcf9b8c9808e6…1715d185fd09bd

3 in → 2 out100.2500 XPM456 B

AXoRaCg1…sWUeov5j AJNyv44i…z4zNEHHy

c77577ee7d76b3…21ced517d31b28

2 in → 2 out39.0400 XPM306 B

ATLD8KHe…yiDLE4zV AdTLo1Cj…gGNNFPrv

Prime Chain Origin

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

5.750 × 10⁹¹(92-digit number)

57508733277674658690…99333875140798728019

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

5.750 × 10⁹¹(92-digit number)

57508733277674658690…99333875140798728019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.750 × 10⁹¹(92-digit number)

57508733277674658690…99333875140798728021

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.150 × 10⁹²(93-digit number)

11501746655534931738…98667750281597456039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.150 × 10⁹²(93-digit number)

11501746655534931738…98667750281597456041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.300 × 10⁹²(93-digit number)

23003493311069863476…97335500563194912079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.300 × 10⁹²(93-digit number)

23003493311069863476…97335500563194912081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

4.600 × 10⁹²(93-digit number)

46006986622139726952…94671001126389824159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 7

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer