Block #71,737

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 8:14:06 PM · Difficulty 8.9935 · 6,724,099 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

14ad1e4b2e2b93bb8c632abbfac4255a7a530b0c3b8e41a2759646a76d608f2d

View on Chainz ↗

Height

#71,737

Difficulty

8.993472

Transactions

Size

394 B

Version

Bits

08fe542b

Nonce

516

Timestamp

7/20/2013, 8:14:06 PM

Confirmations

6,724,099

Mined by

⛏️ P2SHAXSFye4rUycSu1xJ6pmwUfhCbvADf1YWCU

Merkle Root

b76a23183821b4a87ab85a68740fdf771a52ca42864f5dd3b937be903c64e614

Transactions (2)

Coinbase5ae400ac90d002…6dedb7d178d3b3

1 in → 1 out12.3600 XPM110 B

AXSFye4r…ADf1YWCU

070688cb9a06fd…9c50e4e58a0074

1 in → 2 out12.3500 XPM192 B

AdHH4S7H…YBpU1DpD AHg26cej…zKVe9VZ1

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.

4.672 × 10⁹⁹(100-digit number)

46720814310370882928…73746117024161909399

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

4.672 × 10⁹⁹(100-digit number)

46720814310370882928…73746117024161909399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.672 × 10⁹⁹(100-digit number)

46720814310370882928…73746117024161909401

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

9.344 × 10⁹⁹(100-digit number)

93441628620741765857…47492234048323818799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.344 × 10⁹⁹(100-digit number)

93441628620741765857…47492234048323818801

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

1.868 × 10¹⁰⁰(101-digit number)

18688325724148353171…94984468096647637599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.868 × 10¹⁰⁰(101-digit number)

18688325724148353171…94984468096647637601

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

3.737 × 10¹⁰⁰(101-digit number)

37376651448296706343…89968936193295275199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.737 × 10¹⁰⁰(101-digit number)

37376651448296706343…89968936193295275201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

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 — 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 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 × 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