Block #29,681

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 4:19:55 PM · Difficulty 7.9852 · 6,762,032 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5d8a97297b4ec22abbb0990d646ee6ce19d4cca07a52469137e1e557fd0eb30c

View on Chainz ↗

Height

#29,681

Difficulty

7.985212

Transactions

Size

4.76 KB

Version

Bits

07fc36de

Nonce

763

Timestamp

7/13/2013, 4:19:55 PM

Confirmations

6,762,032

Merkle Root

c787d01613c6dbd43f9498574e124d98be4d999750f490218af8e4084f491f89

Transactions (2)

Coinbase90db0c3d6441fd…8c857677bd05f4

1 in → 1 out15.7100 XPM108 B

AaPsctku…zHHMuejv

3c523733edbad2…c5f878e7536e48

40 in → 2 out616.1500 XPM4.56 KB

ARcPSdXD…z5QxbgUx AP2oaAhb…J3GKp2RS

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.

2.825 × 10¹¹⁰(111-digit number)

28251041728540064303…16030902579884386929

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

2.825 × 10¹¹⁰(111-digit number)

28251041728540064303…16030902579884386929

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.825 × 10¹¹⁰(111-digit number)

28251041728540064303…16030902579884386931

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

5.650 × 10¹¹⁰(111-digit number)

56502083457080128607…32061805159768773859

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.650 × 10¹¹⁰(111-digit number)

56502083457080128607…32061805159768773861

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

1.130 × 10¹¹¹(112-digit number)

11300416691416025721…64123610319537547719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.130 × 10¹¹¹(112-digit number)

11300416691416025721…64123610319537547721

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

2.260 × 10¹¹¹(112-digit number)

22600833382832051443…28247220639075095439

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