Block #330,905

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2013, 12:08:56 AM · Difficulty 10.1684 · 6,474,279 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c6c68851aa6553eb4da135462cc9889745eae3195173332b55833372536c3221

View on Chainz ↗

Height

#330,905

Difficulty

10.168382

Transactions

Size

653 B

Version

Bits

0a2b1b1b

Nonce

28,887

Timestamp

12/27/2013, 12:08:56 AM

Confirmations

6,474,279

Mined by

⛏️ P2SHAeZVTXhUPrm5nm3Mdr7XzinsLLzkiAA1i1

Merkle Root

be431e148cb68593b3358d4c2e7ff18b004dbf8682d297870903a1c7f6020dd9

Transactions (3)

Coinbase035f6b5b4913ea…d621043cb149ad

1 in → 1 out9.6800 XPM109 B

AeZVTXhU…zkiAA1i1

84bb71b9db69e8…2b9c9f6445dc76

1 in → 2 out6.0348 XPM226 B

AMw3x3qJ…hsaq8ffo AMu4YTFf…SwFhX9P2

47ff5719eacb4c…48b9caa083a79b

1 in → 2 out8186.8715 XPM227 B

ARSVKsJG…MeRk5uBW AYc5nTAk…nDrM4qK1

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.

1.914 × 10⁹⁶(97-digit number)

19147399684300931705…27634114701945034719

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

1.914 × 10⁹⁶(97-digit number)

19147399684300931705…27634114701945034719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.914 × 10⁹⁶(97-digit number)

19147399684300931705…27634114701945034721

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

3.829 × 10⁹⁶(97-digit number)

38294799368601863411…55268229403890069439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.829 × 10⁹⁶(97-digit number)

38294799368601863411…55268229403890069441

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

7.658 × 10⁹⁶(97-digit number)

76589598737203726823…10536458807780138879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.658 × 10⁹⁶(97-digit number)

76589598737203726823…10536458807780138881

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

1.531 × 10⁹⁷(98-digit number)

15317919747440745364…21072917615560277759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.531 × 10⁹⁷(98-digit number)

15317919747440745364…21072917615560277761

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

3.063 × 10⁹⁷(98-digit number)

30635839494881490729…42145835231120555519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.063 × 10⁹⁷(98-digit number)

30635839494881490729…42145835231120555521

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