Block #427,366

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2014, 8:11:46 AM · Difficulty 10.3471 · 6,399,622 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b04e1b372e17827af8744a80bcb3783e48455f26e2d65858128d37f45e203fe

View on Chainz ↗

Height

#427,366

Difficulty

10.347108

Transactions

Size

61.87 KB

Version

Bits

0a58dc14

Nonce

7,119

Timestamp

3/3/2014, 8:11:46 AM

Confirmations

6,399,622

Mined by

⛏️ fXAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

c81827c162d9e24c14cb13560feaa73b294dab587f68d0f54243bf6a6fb16371

Transactions (2)

Coinbasec88f17dc3525ff…a6f17963bf3a3f

1 in → 24 out9.9900 XPM879 B

AdFLJFhb…bsaVkAyh AcuM7XiJ…5uND8Jce AZqjMFvv…G8aw2zC8 AQFhQpUS…HmKbSyAx AVRMvm7T…6PC6keBx

832052c9b4a98e…39422a92e4233c

421 in → 2 out2500.0100 XPM60.92 KB

ANhugLbe…iU3cfuXU AJ2ubWJ9…tyRWrLat

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.

1.755 × 10⁹⁹(100-digit number)

17550480891661463093…73980770540193609599

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

1.755 × 10⁹⁹(100-digit number)

17550480891661463093…73980770540193609599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.755 × 10⁹⁹(100-digit number)

17550480891661463093…73980770540193609601

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

3.510 × 10⁹⁹(100-digit number)

35100961783322926186…47961541080387219199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.510 × 10⁹⁹(100-digit number)

35100961783322926186…47961541080387219201

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

7.020 × 10⁹⁹(100-digit number)

70201923566645852373…95923082160774438399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.020 × 10⁹⁹(100-digit number)

70201923566645852373…95923082160774438401

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

1.404 × 10¹⁰⁰(101-digit number)

14040384713329170474…91846164321548876799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.404 × 10¹⁰⁰(101-digit number)

14040384713329170474…91846164321548876801

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.808 × 10¹⁰⁰(101-digit number)

28080769426658340949…83692328643097753599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.808 × 10¹⁰⁰(101-digit number)

28080769426658340949…83692328643097753601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #427,366

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