Block #335,028

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/29/2013, 9:53:46 PM · Difficulty 10.1602 · 6,461,457 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e7611d26127ef19e8c8ab18f1aa8062bfc4907d831e877b9e1c8e1b7ee586d48

View on Chainz ↗

Height

#335,028

Difficulty

10.160175

Transactions

Size

653 B

Version

Bits

0a290133

Nonce

273,201

Timestamp

12/29/2013, 9:53:46 PM

Confirmations

6,461,457

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

93d5f14ff49b955f7e70507f1c24dbfd6e846ef2f40988f1ac58ed044775a1b9

Transactions (3)

Coinbase174a55adb218ec…4ee3fb248ad438

1 in → 1 out9.6900 XPM110 B

AeKNrjNj…1NEq95Ta

c6ebe44a25a7aa…6fde22af4c59c9

1 in → 2 out5.4103 XPM226 B

AZ4Yzkkd…mpym1pUs ALGoNmyS…oRwg8sE1

4a89ff6d77294b…cf7e2a6a23abdf

1 in → 2 out3.8353 XPM227 B

ATTkHJqa…bBq6fEeJ AWpXgD8k…K7NvcRLh

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.

4.684 × 10⁹⁴(95-digit number)

46841474087956808933…07825651427460349439

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

4.684 × 10⁹⁴(95-digit number)

46841474087956808933…07825651427460349439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.684 × 10⁹⁴(95-digit number)

46841474087956808933…07825651427460349441

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

9.368 × 10⁹⁴(95-digit number)

93682948175913617867…15651302854920698879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.368 × 10⁹⁴(95-digit number)

93682948175913617867…15651302854920698881

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

1.873 × 10⁹⁵(96-digit number)

18736589635182723573…31302605709841397759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.873 × 10⁹⁵(96-digit number)

18736589635182723573…31302605709841397761

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

3.747 × 10⁹⁵(96-digit number)

37473179270365447146…62605211419682795519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.747 × 10⁹⁵(96-digit number)

37473179270365447146…62605211419682795521

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

7.494 × 10⁹⁵(96-digit number)

74946358540730894293…25210422839365591039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.494 × 10⁹⁵(96-digit number)

74946358540730894293…25210422839365591041

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