Block #349,383

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/8/2014, 9:31:24 AM · Difficulty 10.2723 · 6,446,586 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ef73b759915aed50482026da0a3b92730ca6625d018a19bb8bdc1cd9ccbcfea

View on Chainz ↗

Height

#349,383

Difficulty

10.272255

Transactions

Size

1.05 KB

Version

Bits

0a45b287

Nonce

18,961

Timestamp

1/8/2014, 9:31:24 AM

Confirmations

6,446,586

Mined by

⛏️ TaRfAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

92dc4afab7651022c45dbb871c269ef8f857831f15ed94a42c58a9734f0bb5c3

Transactions (1)

Coinbase92dc4afab76510…58a9734f0bb5c3

1 in → 27 out9.4600 XPM981 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AUnkFe8H…fvenjA4X AZV4TwxQ…8JnQqSoH

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.

3.103 × 10⁹³(94-digit number)

31037481750713578421…61900008673156364799

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

3.103 × 10⁹³(94-digit number)

31037481750713578421…61900008673156364799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.103 × 10⁹³(94-digit number)

31037481750713578421…61900008673156364801

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

6.207 × 10⁹³(94-digit number)

62074963501427156843…23800017346312729599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.207 × 10⁹³(94-digit number)

62074963501427156843…23800017346312729601

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

1.241 × 10⁹⁴(95-digit number)

12414992700285431368…47600034692625459199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.241 × 10⁹⁴(95-digit number)

12414992700285431368…47600034692625459201

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

2.482 × 10⁹⁴(95-digit number)

24829985400570862737…95200069385250918399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.482 × 10⁹⁴(95-digit number)

24829985400570862737…95200069385250918401

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

4.965 × 10⁹⁴(95-digit number)

49659970801141725474…90400138770501836799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.965 × 10⁹⁴(95-digit number)

49659970801141725474…90400138770501836801

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