Block #442,123

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2014, 2:43:07 PM · Difficulty 10.3519 · 6,365,237 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0327d43cbbd2d0d6c5390d3378cb9e1c0d904c2a4204ba199ce5c57db48f7f1e

View on Chainz ↗

Height

#442,123

Difficulty

10.351897

Transactions

Size

11.62 KB

Version

Bits

0a5a15eb

Nonce

74,651

Timestamp

3/13/2014, 2:43:07 PM

Confirmations

6,365,237

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

2e0bc99365011419448c846cfe58cbff0ee250fb98297e32bfc21918fb440c0d

Transactions (5)

Coinbase7fb6d605c4f0e1…44b72a22c52ad9

1 in → 1 out9.4500 XPM116 B

AbwWkWZt…kawDhufa

04183af30e0779…7272068ba78376

4 in → 11 out37.2500 XPM840 B

AM4zUqtZ…qoQ34B2Y ARi5oPMC…yhqk7g4j AL9UZuKj…g3Q3eciV AeKNrjNj…1NEq95Ta AKgMuH2h…bnM6fTBV

96edf09b190d68…6bc9a1876c8e92

6 in → 1 out12.0245 XPM932 B

AaqD98At…sN5nRXUY

56e08968a232f6…0a8c595dae83c5

65 in → 2 out233.8374 XPM9.46 KB

AN1Tm8m9…suwySgLN AWeBQtWf…H1aW2bZH

a3d75c3b97f652…302f4d583bcb9d

1 in → 2 out2.1962 XPM227 B

AX6A8SiQ…vR628xiF AMZWH4L3…joZnz5mc

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.

4.414 × 10⁹⁷(98-digit number)

44140781196524810480…47772029617800365279

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

4.414 × 10⁹⁷(98-digit number)

44140781196524810480…47772029617800365279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.414 × 10⁹⁷(98-digit number)

44140781196524810480…47772029617800365281

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

8.828 × 10⁹⁷(98-digit number)

88281562393049620960…95544059235600730559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.828 × 10⁹⁷(98-digit number)

88281562393049620960…95544059235600730561

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

1.765 × 10⁹⁸(99-digit number)

17656312478609924192…91088118471201461119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.765 × 10⁹⁸(99-digit number)

17656312478609924192…91088118471201461121

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

3.531 × 10⁹⁸(99-digit number)

35312624957219848384…82176236942402922239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.531 × 10⁹⁸(99-digit number)

35312624957219848384…82176236942402922241

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

7.062 × 10⁹⁸(99-digit number)

70625249914439696768…64352473884805844479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.062 × 10⁹⁸(99-digit number)

70625249914439696768…64352473884805844481

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 #442,123

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