Block #366,367

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/19/2014, 8:59:51 AM · Difficulty 10.4298 · 6,446,368 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f4fa55be698ee1f708dfa5c84e93804ba85601e569b8ac80a347c0a5ca14457e

View on Chainz ↗

Height

#366,367

Difficulty

10.429792

Transactions

Size

871 B

Version

Bits

0a6e06d2

Nonce

196,269

Timestamp

1/19/2014, 8:59:51 AM

Confirmations

6,446,368

Mined by

⛏️ P2SHAa9msepkg3E2mBgMWBhZMJrHEPHXnQtw8B

Merkle Root

cb5fad4490dbad631187fe903873ae50c5503c6a9d5b753ad29d6137bb9cd7e1

Transactions (2)

Coinbase3bde154090d793…c7130ca7efe66c

1 in → 1 out9.1900 XPM109 B

Aa9msepk…HXnQtw8B

cad086a1ffa401…12b2e414bbcf8f

4 in → 2 out6.5107 XPM672 B

AXeX8YRZ…yUoZePNY AJ2ew3S7…EHPTaiPf

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.

5.135 × 10⁹⁵(96-digit number)

51359036774802404138…61267112433627511699

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

5.135 × 10⁹⁵(96-digit number)

51359036774802404138…61267112433627511699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.135 × 10⁹⁵(96-digit number)

51359036774802404138…61267112433627511701

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

1.027 × 10⁹⁶(97-digit number)

10271807354960480827…22534224867255023399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.027 × 10⁹⁶(97-digit number)

10271807354960480827…22534224867255023401

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

2.054 × 10⁹⁶(97-digit number)

20543614709920961655…45068449734510046799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.054 × 10⁹⁶(97-digit number)

20543614709920961655…45068449734510046801

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

4.108 × 10⁹⁶(97-digit number)

41087229419841923311…90136899469020093599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.108 × 10⁹⁶(97-digit number)

41087229419841923311…90136899469020093601

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

8.217 × 10⁹⁶(97-digit number)

82174458839683846622…80273798938040187199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.217 × 10⁹⁶(97-digit number)

82174458839683846622…80273798938040187201

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 #366,367

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