Block #430,638

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/5/2014, 3:22:22 PM · Difficulty 10.3448 · 6,378,628 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa5b01aa900043fb6c01429aa08400dfab196b9c40f52593c0a4a80adcf88cf0

View on Chainz ↗

Height

#430,638

Difficulty

10.344762

Transactions

Size

968 B

Version

Bits

0a584256

Nonce

111,431

Timestamp

3/5/2014, 3:22:22 PM

Confirmations

6,378,628

Mined by

⛏️ .aSAAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

bc0b2aca9ec7b1e3c95724b54f9f535ffa0445fe8ccb77d114ceb05d246af719

Transactions (1)

Coinbasebc0b2aca9ec7b1…ceb05d246af719

1 in → 24 out9.3300 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

1.237 × 10⁹²(93-digit number)

12374706960845473732…46358847519590446719

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

1.237 × 10⁹²(93-digit number)

12374706960845473732…46358847519590446719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.237 × 10⁹²(93-digit number)

12374706960845473732…46358847519590446721

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

2.474 × 10⁹²(93-digit number)

24749413921690947465…92717695039180893439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.474 × 10⁹²(93-digit number)

24749413921690947465…92717695039180893441

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

4.949 × 10⁹²(93-digit number)

49498827843381894931…85435390078361786879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.949 × 10⁹²(93-digit number)

49498827843381894931…85435390078361786881

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

9.899 × 10⁹²(93-digit number)

98997655686763789862…70870780156723573759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.899 × 10⁹²(93-digit number)

98997655686763789862…70870780156723573761

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

1.979 × 10⁹³(94-digit number)

19799531137352757972…41741560313447147519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.979 × 10⁹³(94-digit number)

19799531137352757972…41741560313447147521

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 #430,638

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