Block #334,998

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/29/2013, 9:22:07 PM · Difficulty 10.1604 · 6,482,092 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8c13ea56868da7063564fae5a651ba333bf6589f4ee09a18566f6fee68e0e6a6

View on Chainz ↗

Height

#334,998

Difficulty

10.160417

Transactions

Size

428 B

Version

Bits

0a29111e

Nonce

192,105

Timestamp

12/29/2013, 9:22:07 PM

Confirmations

6,482,092

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

24fb7c619ed8d3908aa6ecaad80fa9a38fb0fcab4de763ecf0d8f18933d729b5

Transactions (2)

Coinbasea6dd37e6b19d23…b49c6d48359bad

1 in → 1 out9.6800 XPM110 B

AeKNrjNj…1NEq95Ta

78936dee63c92e…41f222b49f2463

1 in → 2 out7.0413 XPM226 B

AajxZyRM…4V1FapnA AbUnrgvg…1wBMZ3Eu

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.

4.719 × 10⁹⁸(99-digit number)

47195570209829050462…37322913637936812599

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

4.719 × 10⁹⁸(99-digit number)

47195570209829050462…37322913637936812599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.719 × 10⁹⁸(99-digit number)

47195570209829050462…37322913637936812601

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

9.439 × 10⁹⁸(99-digit number)

94391140419658100925…74645827275873625199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.439 × 10⁹⁸(99-digit number)

94391140419658100925…74645827275873625201

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

1.887 × 10⁹⁹(100-digit number)

18878228083931620185…49291654551747250399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.887 × 10⁹⁹(100-digit number)

18878228083931620185…49291654551747250401

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

3.775 × 10⁹⁹(100-digit number)

37756456167863240370…98583309103494500799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.775 × 10⁹⁹(100-digit number)

37756456167863240370…98583309103494500801

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

7.551 × 10⁹⁹(100-digit number)

75512912335726480740…97166618206989001599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.551 × 10⁹⁹(100-digit number)

75512912335726480740…97166618206989001601

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 #334,998

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