Block #57,572

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/17/2013, 3:30:12 PM · Difficulty 8.9552 · 6,760,270 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ae5e098221af1371a28fcc964cc4e5db59e9004c12b08999e75a6ff2e432d121

View on Chainz ↗

Height

#57,572

Difficulty

8.955205

Transactions

Size

577 B

Version

Bits

08f4884e

Nonce

Timestamp

7/17/2013, 3:30:12 PM

Confirmations

6,760,270

Mined by

⛏️ P2SHAMJGTwKci9EcXYd1pxeLH8kwwRk18kkTir

Merkle Root

cb109322fdf1999c33a8581c358081a96a30141ce63a885d40e2a59e9ca34aac

Transactions (2)

Coinbase9898bcb8c3c629…856fb2776d45e8

1 in → 1 out12.4600 XPM110 B

AMJGTwKc…k18kkTir

b13c483dcb5db2…8f773df7b7b5f6

2 in → 2 out153.2600 XPM374 B

AXqLdXqC…P4VUDvUP AVBeKVCF…FPZ88qAM

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.

3.692 × 10¹⁰¹(102-digit number)

36926571261451364619…76635363526910232919

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

3.692 × 10¹⁰¹(102-digit number)

36926571261451364619…76635363526910232919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.692 × 10¹⁰¹(102-digit number)

36926571261451364619…76635363526910232921

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

7.385 × 10¹⁰¹(102-digit number)

73853142522902729238…53270727053820465839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.385 × 10¹⁰¹(102-digit number)

73853142522902729238…53270727053820465841

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

1.477 × 10¹⁰²(103-digit number)

14770628504580545847…06541454107640931679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.477 × 10¹⁰²(103-digit number)

14770628504580545847…06541454107640931681

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

2.954 × 10¹⁰²(103-digit number)

29541257009161091695…13082908215281863359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.954 × 10¹⁰²(103-digit number)

29541257009161091695…13082908215281863361

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

Block #57,572

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