Block #432,399

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 9:05:25 PM · Difficulty 10.3430 · 6,369,134 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7a9ccff1cbd3620d1b400ddf6bc28ff3cb22bd86191e2002753d0d267873915

View on Chainz ↗

Height

#432,399

Difficulty

10.342953

Transactions

Size

1.10 KB

Version

Bits

0a57cbc8

Nonce

31,403

Timestamp

3/6/2014, 9:05:25 PM

Confirmations

6,369,134

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

6a0553a983dfc3e7d7b3b3ad857406122a56a1eb8511d5b9ddb6747e257711fb

Transactions (2)

Coinbase508cd2082e8f1d…69047d81d2a4ea

1 in → 23 out9.3400 XPM845 B

AdFLJFhb…bsaVkAyh AQFhQpUS…HmKbSyAx ASgUri65…C7NLcyBg AVRMvm7T…6PC6keBx Acs9SHrk…QJSB8SFG

b5918c115af299…062e5d7ec86bb0

1 in → 1 out2.9903 XPM193 B

AUfB8F2S…GSdUavUD

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.

7.056 × 10⁹⁸(99-digit number)

70567653601030597043…55691844569062629459

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

7.056 × 10⁹⁸(99-digit number)

70567653601030597043…55691844569062629459

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.056 × 10⁹⁸(99-digit number)

70567653601030597043…55691844569062629461

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

1.411 × 10⁹⁹(100-digit number)

14113530720206119408…11383689138125258919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.411 × 10⁹⁹(100-digit number)

14113530720206119408…11383689138125258921

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

2.822 × 10⁹⁹(100-digit number)

28227061440412238817…22767378276250517839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.822 × 10⁹⁹(100-digit number)

28227061440412238817…22767378276250517841

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

5.645 × 10⁹⁹(100-digit number)

56454122880824477635…45534756552501035679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.645 × 10⁹⁹(100-digit number)

56454122880824477635…45534756552501035681

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

1.129 × 10¹⁰⁰(101-digit number)

11290824576164895527…91069513105002071359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.129 × 10¹⁰⁰(101-digit number)

11290824576164895527…91069513105002071361

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