Block #339,499

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2014, 3:56:51 AM · Difficulty 10.1260 · 6,468,682 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

68082976dd9ef0c3c2121a1e67038045348ffda57d2447291d4702f943aaed72

View on Chainz ↗

Height

#339,499

Difficulty

10.125966

Transactions

Size

1004 B

Version

Bits

0a203f4f

Nonce

15,094

Timestamp

1/2/2014, 3:56:51 AM

Confirmations

6,468,682

Mined by

⛏️ +.aRhAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

e54ad11889ba18131a9348da4bde85bbf247532d3eab86f2db8f410ac874b7b2

Transactions (1)

Coinbasee54ad11889ba18…8f410ac874b7b2

1 in → 25 out9.7369 XPM913 B

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

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.

1.656 × 10⁹⁶(97-digit number)

16565483721759544455…38002196589888026879

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

1.656 × 10⁹⁶(97-digit number)

16565483721759544455…38002196589888026879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.656 × 10⁹⁶(97-digit number)

16565483721759544455…38002196589888026881

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

3.313 × 10⁹⁶(97-digit number)

33130967443519088910…76004393179776053759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.313 × 10⁹⁶(97-digit number)

33130967443519088910…76004393179776053761

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

6.626 × 10⁹⁶(97-digit number)

66261934887038177821…52008786359552107519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.626 × 10⁹⁶(97-digit number)

66261934887038177821…52008786359552107521

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

1.325 × 10⁹⁷(98-digit number)

13252386977407635564…04017572719104215039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.325 × 10⁹⁷(98-digit number)

13252386977407635564…04017572719104215041

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

2.650 × 10⁹⁷(98-digit number)

26504773954815271128…08035145438208430079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.650 × 10⁹⁷(98-digit number)

26504773954815271128…08035145438208430081

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 #339,499

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