Block #394,716

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2014, 4:20:24 AM · Difficulty 10.4187 · 6,416,108 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7f3dde20e7c3c335af3d3250fa6f6f48ed01ba4c3c1d19e8f49c6b48c1dd1c8

View on Chainz ↗

Height

#394,716

Difficulty

10.418743

Transactions

Size

1.90 KB

Version

Bits

0a6b32b7

Nonce

299,741

Timestamp

2/8/2014, 4:20:24 AM

Confirmations

6,416,108

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

433321bf8d4e85977e4ab29a15fd6cb2f29fbf8e4a4ff9b91c591ad6ee2afb24

Transactions (3)

Coinbaseb33b11833aeb6d…990728afddcab2

1 in → 1 out9.2338 XPM110 B

AeKNrjNj…1NEq95Ta

53cf0f09f1e811…5b787a241f56cb

7 in → 1 out6.4500 XPM1.06 KB

AaiwcnbW…b8UooEEu

62ee9507cc0600…96833b408e0cf4

3 in → 9 out27.5500 XPM659 B

AeKNrjNj…1NEq95Ta AKi9dGop…vQ9PKwNj AS791b91…2oFChkDv AQPsZ8Wr…JMqn2uxw AYiuPkxV…9nUvdUg1

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.

7.750 × 10¹⁰¹(102-digit number)

77508743611349969233…77790855754913320779

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

7.750 × 10¹⁰¹(102-digit number)

77508743611349969233…77790855754913320779

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.750 × 10¹⁰¹(102-digit number)

77508743611349969233…77790855754913320781

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

1.550 × 10¹⁰²(103-digit number)

15501748722269993846…55581711509826641559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.550 × 10¹⁰²(103-digit number)

15501748722269993846…55581711509826641561

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

3.100 × 10¹⁰²(103-digit number)

31003497444539987693…11163423019653283119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.100 × 10¹⁰²(103-digit number)

31003497444539987693…11163423019653283121

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

6.200 × 10¹⁰²(103-digit number)

62006994889079975386…22326846039306566239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.200 × 10¹⁰²(103-digit number)

62006994889079975386…22326846039306566241

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

1.240 × 10¹⁰³(104-digit number)

12401398977815995077…44653692078613132479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.240 × 10¹⁰³(104-digit number)

12401398977815995077…44653692078613132481

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 #394,716

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