Block #328,104

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/25/2013, 12:42:59 AM · Difficulty 10.1748 · 6,475,214 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c6533e789618ebe83f1f78ab116be492fe748807331ed3d7e016d7279d760ff8

View on Chainz ↗

Height

#328,104

Difficulty

10.174816

Transactions

Size

1.23 KB

Version

Bits

0a2cc0c1

Nonce

24,353

Timestamp

12/25/2013, 12:42:59 AM

Confirmations

6,475,214

Mined by

⛏️ aR*=QAG5YAjechu8kNZ5eyyVJVz1YnBVhA4Aeh1

Merkle Root

53658b2549fa7aae33f95305114c3149e7e8484ee3772246ed4b1efd350ab24e

Transactions (2)

Coinbase7009b785bdb4a5…91897d9173fb6f

1 in → 26 out9.6400 XPM947 B

AG5YAjec…VhA4Aeh1 Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AayReikY…2HAC42fs AFutDVqJ…TJTJj6UF

de930bc9ad7de4…235b5b80bdcbba

1 in → 2 out5.4415 XPM226 B

AUKEZeRy…VkG2RBUJ AJHMeUzo…o5EQTvMg

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.

2.729 × 10⁹⁷(98-digit number)

27298575488449259419…49327041198752770159

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

2.729 × 10⁹⁷(98-digit number)

27298575488449259419…49327041198752770159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.729 × 10⁹⁷(98-digit number)

27298575488449259419…49327041198752770161

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

5.459 × 10⁹⁷(98-digit number)

54597150976898518838…98654082397505540319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.459 × 10⁹⁷(98-digit number)

54597150976898518838…98654082397505540321

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

1.091 × 10⁹⁸(99-digit number)

10919430195379703767…97308164795011080639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.091 × 10⁹⁸(99-digit number)

10919430195379703767…97308164795011080641

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

2.183 × 10⁹⁸(99-digit number)

21838860390759407535…94616329590022161279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.183 × 10⁹⁸(99-digit number)

21838860390759407535…94616329590022161281

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

4.367 × 10⁹⁸(99-digit number)

43677720781518815070…89232659180044322559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.367 × 10⁹⁸(99-digit number)

43677720781518815070…89232659180044322561

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