Block #350,323

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/8/2014, 11:28:19 PM · Difficulty 10.2872 · 6,476,581 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

73fb70082d03437deed34bab5ad5393819735fa077294737d76bc6c9637ad93a

View on Chainz ↗

Height

#350,323

Difficulty

10.287201

Transactions

Size

1.05 KB

Version

Bits

0a498604

Nonce

16,991

Timestamp

1/8/2014, 11:28:19 PM

Confirmations

6,476,581

Mined by

⛏️ sXaR!AUnkFe8HFyvLomfA4aQ3rU4psJfvenjA4X

Merkle Root

5febd76f68314df8cdb5b7995d89b8ff3ceb3c645460e3f625edc0933c27cf2a

Transactions (1)

Coinbase5febd76f68314d…edc0933c27cf2a

1 in → 27 out9.4300 XPM981 B

AUnkFe8H…fvenjA4X AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR ARck9uUe…jQe3uJMp AczNP7Qa…nfcLAodi

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.

2.276 × 10⁹⁴(95-digit number)

22766332358476169191…59275415449913663999

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

2.276 × 10⁹⁴(95-digit number)

22766332358476169191…59275415449913663999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.276 × 10⁹⁴(95-digit number)

22766332358476169191…59275415449913664001

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

4.553 × 10⁹⁴(95-digit number)

45532664716952338383…18550830899827327999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.553 × 10⁹⁴(95-digit number)

45532664716952338383…18550830899827328001

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

9.106 × 10⁹⁴(95-digit number)

91065329433904676766…37101661799654655999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.106 × 10⁹⁴(95-digit number)

91065329433904676766…37101661799654656001

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

1.821 × 10⁹⁵(96-digit number)

18213065886780935353…74203323599309311999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.821 × 10⁹⁵(96-digit number)

18213065886780935353…74203323599309312001

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

3.642 × 10⁹⁵(96-digit number)

36426131773561870706…48406647198618623999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.642 × 10⁹⁵(96-digit number)

36426131773561870706…48406647198618624001

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 #350,323

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