Block #472,431

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2014, 7:00:24 AM · Difficulty 10.4334 · 6,336,209 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e2c6f3f34fbb4944962bab5f0e7f6fe1f755f2b0093b145cf111fa7bca020144

View on Chainz ↗

Height

#472,431

Difficulty

10.433426

Transactions

Size

901 B

Version

Bits

0a6ef4fc

Nonce

50,805

Timestamp

4/3/2014, 7:00:24 AM

Confirmations

6,336,209

Mined by

⛏️ o5SAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

1d637e017cea395b8ab23e4c3d66455f4dbfbd5211174ffeb3e58747592ff4ba

Transactions (1)

Coinbase1d637e017cea39…e58747592ff4ba

1 in → 22 out9.1700 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AUFKXvnz…342ApNcm AZ34NcPy…8FPeFjPV AZdy7tMB…bWoKDJVg

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.

1.906 × 10⁹⁵(96-digit number)

19069144906018074739…43674462149661244159

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

1.906 × 10⁹⁵(96-digit number)

19069144906018074739…43674462149661244159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.906 × 10⁹⁵(96-digit number)

19069144906018074739…43674462149661244161

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

3.813 × 10⁹⁵(96-digit number)

38138289812036149479…87348924299322488319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.813 × 10⁹⁵(96-digit number)

38138289812036149479…87348924299322488321

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

7.627 × 10⁹⁵(96-digit number)

76276579624072298958…74697848598644976639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.627 × 10⁹⁵(96-digit number)

76276579624072298958…74697848598644976641

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

1.525 × 10⁹⁶(97-digit number)

15255315924814459791…49395697197289953279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.525 × 10⁹⁶(97-digit number)

15255315924814459791…49395697197289953281

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

3.051 × 10⁹⁶(97-digit number)

30510631849628919583…98791394394579906559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.051 × 10⁹⁶(97-digit number)

30510631849628919583…98791394394579906561

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 #472,431

Cookie Preferences