Block #349,415

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/8/2014, 9:56:31 AM · Difficulty 10.2732 · 6,455,630 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

68fb424f4b383fd3e68dd17c1ad0e16a2707ca8eebd184d8ddaea871a241e27a

View on Chainz ↗

Height

#349,415

Difficulty

10.273233

Transactions

Size

2.19 KB

Version

Bits

0a45f2a1

Nonce

3,242

Timestamp

1/8/2014, 9:56:31 AM

Confirmations

6,455,630

Mined by

⛏️ TaRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c2db75c208fa69ba964f307eb4aedc73ea937509d636be19d584624f5b9305b1

Transactions (2)

Coinbasee6d240f5ee7cfe…eaf1252e436d42

1 in → 23 out9.4600 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 APeshfYV…3PKcKMKH AQ8QAT3J…rCFKuVbR AZV4TwxQ…8JnQqSoH

e8618e3eda2660…212e424368ecc7

6 in → 18 out57.6800 XPM1.27 KB

Aab4hrNV…XibmcGYq AeKNrjNj…1NEq95Ta AbvJyfpy…akhhXHLz AZvBBxNM…gmhEg6pv ARq3HvGe…MJHG3U4J

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.

2.789 × 10⁹⁵(96-digit number)

27899001522646688195…45721441400522350079

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

2.789 × 10⁹⁵(96-digit number)

27899001522646688195…45721441400522350079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.789 × 10⁹⁵(96-digit number)

27899001522646688195…45721441400522350081

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

5.579 × 10⁹⁵(96-digit number)

55798003045293376390…91442882801044700159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.579 × 10⁹⁵(96-digit number)

55798003045293376390…91442882801044700161

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

1.115 × 10⁹⁶(97-digit number)

11159600609058675278…82885765602089400319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.115 × 10⁹⁶(97-digit number)

11159600609058675278…82885765602089400321

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

2.231 × 10⁹⁶(97-digit number)

22319201218117350556…65771531204178800639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.231 × 10⁹⁶(97-digit number)

22319201218117350556…65771531204178800641

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

4.463 × 10⁹⁶(97-digit number)

44638402436234701112…31543062408357601279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.463 × 10⁹⁶(97-digit number)

44638402436234701112…31543062408357601281

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