Block #343,320

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/4/2014, 3:00:43 PM · Difficulty 10.1737 · 6,455,107 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ddba002209b144209c0bf0a1aa91de6cd64fec86c5036f7e6b78fb395efc3b52

View on Chainz ↗

Height

#343,320

Difficulty

10.173677

Transactions

Size

1.08 KB

Version

Bits

0a2c7617

Nonce

1,310

Timestamp

1/4/2014, 3:00:43 PM

Confirmations

6,455,107

Mined by

⛏️ =aR!QAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

81556135d21dd509d50f440bf3007e4fec4cd550410d8309b7083f81d76cf832

Transactions (1)

Coinbase81556135d21dd5…083f81d76cf832

1 in → 28 out9.6300 XPM1015 B

AQvZBsUo…hppgRZTJ AQ8QAT3J…rCFKuVbR AZemWJAo…6jhDtieG AcuM7XiJ…5uND8Jce Af5qanha…3S4JZCTK

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.

2.496 × 10⁹⁴(95-digit number)

24960144857236389697…11714536379604894719

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

2.496 × 10⁹⁴(95-digit number)

24960144857236389697…11714536379604894719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.496 × 10⁹⁴(95-digit number)

24960144857236389697…11714536379604894721

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

4.992 × 10⁹⁴(95-digit number)

49920289714472779394…23429072759209789439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.992 × 10⁹⁴(95-digit number)

49920289714472779394…23429072759209789441

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

9.984 × 10⁹⁴(95-digit number)

99840579428945558788…46858145518419578879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.984 × 10⁹⁴(95-digit number)

99840579428945558788…46858145518419578881

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

1.996 × 10⁹⁵(96-digit number)

19968115885789111757…93716291036839157759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.996 × 10⁹⁵(96-digit number)

19968115885789111757…93716291036839157761

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

3.993 × 10⁹⁵(96-digit number)

39936231771578223515…87432582073678315519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.993 × 10⁹⁵(96-digit number)

39936231771578223515…87432582073678315521

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