Block #333,489

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/28/2013, 8:21:06 PM · Difficulty 10.1608 · 6,475,937 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c202399fdf1fa9d40baba4da814062ad99645080327d5891d6168dabfbc01d6e

View on Chainz ↗

Height

#333,489

Difficulty

10.160803

Transactions

Size

1.85 KB

Version

Bits

0a292a6b

Nonce

9,243

Timestamp

12/28/2013, 8:21:06 PM

Confirmations

6,475,937

Mined by

⛏️ aRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

1a89e9817774ff560b00f4bb7efea5a08f66683871b54c6ad6791f21efd624c7

Transactions (4)

Coinbase0fce85e61f1bb4…10734cf7cefa1a

1 in → 27 out9.6700 XPM981 B

AQwRN8bE…V8PsTcY9 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7

b9389b453b74c6…d78fb0c3fb957a

1 in → 2 out2438.0686 XPM227 B

AKW9boMS…T2uoRRgS AWjhr1Ns…WDsRswcK

2d839b1ffbea9b…cef35a924f93fb

2 in → 2 out5.8168 XPM373 B

AMUfhz8J…8j8QkMts AQHTm9cM…BJXTkf1C

723bbb75fe1863…fdcc782361bca6

1 in → 2 out5.0101 XPM226 B

AUVJV4Um…Jv64E1GN AWs4ZGyE…ihXCJBTe

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.

3.410 × 10⁹⁶(97-digit number)

34100867455669736042…89228090109195473399

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

3.410 × 10⁹⁶(97-digit number)

34100867455669736042…89228090109195473399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.410 × 10⁹⁶(97-digit number)

34100867455669736042…89228090109195473401

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

6.820 × 10⁹⁶(97-digit number)

68201734911339472084…78456180218390946799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.820 × 10⁹⁶(97-digit number)

68201734911339472084…78456180218390946801

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

1.364 × 10⁹⁷(98-digit number)

13640346982267894416…56912360436781893599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.364 × 10⁹⁷(98-digit number)

13640346982267894416…56912360436781893601

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

2.728 × 10⁹⁷(98-digit number)

27280693964535788833…13824720873563787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.728 × 10⁹⁷(98-digit number)

27280693964535788833…13824720873563787201

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

5.456 × 10⁹⁷(98-digit number)

54561387929071577667…27649441747127574399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.456 × 10⁹⁷(98-digit number)

54561387929071577667…27649441747127574401

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 #333,489

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