Block #330,591

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/26/2013, 7:04:46 PM · Difficulty 10.1659 · 6,487,384 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

641663037618bc00db569637b77996d50a86eb49b4c8b9b9a3fe8b351a13a828

View on Chainz ↗

Height

#330,591

Difficulty

10.165875

Transactions

Size

797 B

Version

Bits

0a2a76c2

Nonce

134,574

Timestamp

12/26/2013, 7:04:46 PM

Confirmations

6,487,384

Mined by

⛏️ P2SHAboLCEinjd2NEztYnSiSQhBW9P7XjxSAfu

Merkle Root

1b7d9081e56d47d94365372c7c285e1885d5272756a04cfd7ca35e309d488936

Transactions (3)

Coinbase6150264250a272…83f582ee19d62d

1 in → 1 out9.6800 XPM109 B

AboLCEin…7XjxSAfu

e23f86ffcdd6c5…60a19d1bf3f12d

1 in → 2 out4.3352 XPM226 B

AWnWeXCV…MXcHULuY ARTcaCVH…LMYVgsg5

b1b8409d3882f3…92a61e8df89966

2 in → 2 out2.1707 XPM373 B

AKUEaUvA…6nAqWbP5 AVcHk5Qx…rRZhc9fb

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.

9.832 × 10⁹¹(92-digit number)

98329049673553561350…72129573974246355199

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

9.832 × 10⁹¹(92-digit number)

98329049673553561350…72129573974246355199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.832 × 10⁹¹(92-digit number)

98329049673553561350…72129573974246355201

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

1.966 × 10⁹²(93-digit number)

19665809934710712270…44259147948492710399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.966 × 10⁹²(93-digit number)

19665809934710712270…44259147948492710401

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

3.933 × 10⁹²(93-digit number)

39331619869421424540…88518295896985420799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.933 × 10⁹²(93-digit number)

39331619869421424540…88518295896985420801

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

7.866 × 10⁹²(93-digit number)

78663239738842849080…77036591793970841599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.866 × 10⁹²(93-digit number)

78663239738842849080…77036591793970841601

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

1.573 × 10⁹³(94-digit number)

15732647947768569816…54073183587941683199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.573 × 10⁹³(94-digit number)

15732647947768569816…54073183587941683201

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 #330,591

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