Block #337,846

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 11:58:36 PM · Difficulty 10.1294 · 6,506,577 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8f0c86f54e7e942f79cd4577c1f7fe59fe8764b01f9ad41c84dcc06ae8206464

View on Chainz ↗

Height

#337,846

Difficulty

10.129448

Transactions

Size

1.05 KB

Version

Bits

0a21237c

Nonce

521,773

Timestamp

12/31/2013, 11:58:36 PM

Confirmations

6,506,577

Mined by

⛏️ 'aRYAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

03b3a4ce57544e0b9c906f992269dce5afe46f44c1fff5cb2f11923ba7c1b68f

Transactions (1)

Coinbase03b3a4ce57544e…11923ba7c1b68f

1 in → 27 out9.7300 XPM981 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.

9.863 × 10⁹⁵(96-digit number)

98637239398939475582…92074292178374290219

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

9.863 × 10⁹⁵(96-digit number)

98637239398939475582…92074292178374290219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.863 × 10⁹⁵(96-digit number)

98637239398939475582…92074292178374290221

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

1.972 × 10⁹⁶(97-digit number)

19727447879787895116…84148584356748580439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.972 × 10⁹⁶(97-digit number)

19727447879787895116…84148584356748580441

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

3.945 × 10⁹⁶(97-digit number)

39454895759575790233…68297168713497160879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.945 × 10⁹⁶(97-digit number)

39454895759575790233…68297168713497160881

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

7.890 × 10⁹⁶(97-digit number)

78909791519151580466…36594337426994321759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.890 × 10⁹⁶(97-digit number)

78909791519151580466…36594337426994321761

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

1.578 × 10⁹⁷(98-digit number)

15781958303830316093…73188674853988643519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.578 × 10⁹⁷(98-digit number)

15781958303830316093…73188674853988643521

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 #337,846

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