Block #384,386

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/1/2014, 2:07:13 AM · Difficulty 10.4013 · 6,426,607 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef047b83ec833ebd3aaee27b7439e35841736b36681725f96d3fbe72e036905f

View on Chainz ↗

Height

#384,386

Difficulty

10.401301

Transactions

Size

230 B

Version

Bits

0a66bbb0

Nonce

19,409

Timestamp

2/1/2014, 2:07:13 AM

Confirmations

6,426,607

Mined by

⛏️ P2SHAN9iEquXMLkQ4kBwmAbtH5ubSEJ6V8wYsN

Merkle Root

2f207216e404e5a1281a151514bd8db4ff1423b1684a3c6a26ebb971a0de8cf9

Transactions (1)

Coinbase2f207216e404e5…ebb971a0de8cf9

1 in → 2 out9.2300 XPM136 B

AN9iEquX…J6V8wYsN Abiw8n3q…ZnZfgvQW

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.

1.276 × 10¹⁰⁵(106-digit number)

12761432654309880963…41501931195778974719

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

1.276 × 10¹⁰⁵(106-digit number)

12761432654309880963…41501931195778974719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.276 × 10¹⁰⁵(106-digit number)

12761432654309880963…41501931195778974721

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

2.552 × 10¹⁰⁵(106-digit number)

25522865308619761926…83003862391557949439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.552 × 10¹⁰⁵(106-digit number)

25522865308619761926…83003862391557949441

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

5.104 × 10¹⁰⁵(106-digit number)

51045730617239523853…66007724783115898879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.104 × 10¹⁰⁵(106-digit number)

51045730617239523853…66007724783115898881

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

1.020 × 10¹⁰⁶(107-digit number)

10209146123447904770…32015449566231797759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.020 × 10¹⁰⁶(107-digit number)

10209146123447904770…32015449566231797761

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

2.041 × 10¹⁰⁶(107-digit number)

20418292246895809541…64030899132463595519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.041 × 10¹⁰⁶(107-digit number)

20418292246895809541…64030899132463595521

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 #384,386

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