Block #384,438

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/1/2014, 2:58:21 AM · Difficulty 10.4015 · 6,411,348 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de359b0c13e4cc1af940aaf08423d9f0220e3a0d4d8d59e906ff99614b81509b

View on Chainz ↗

Height

#384,438

Difficulty

10.401519

Transactions

Size

2.46 KB

Version

Bits

0a66c9f4

Nonce

76,300

Timestamp

2/1/2014, 2:58:21 AM

Confirmations

6,411,348

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

ed2f54deee2740ea110cc4b4c23b85689a08f27323a923df3857d40897c0941c

Transactions (3)

Coinbase718193334eec0a…1d1224b072653d

1 in → 1 out9.2700 XPM110 B

AeKNrjNj…1NEq95Ta

31262cb6e7efe3…ab15a47a27fe6e

5 in → 15 out46.2100 XPM1.07 KB

AeKNrjNj…1NEq95Ta ASj2ErvS…LSxKt2FJ ANmux1Dd…2JA5FHGY ATsDdfHK…1W4qXNRm APeoSKP6…QVsJJKDK

7c2b215993a549…b1351b19cee66b

8 in → 1 out2.5187 XPM1.20 KB

AeQtvLpS…fPJ4mzQM

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.

1.834 × 10⁹⁸(99-digit number)

18342423430913938750…42815170848093405189

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

1.834 × 10⁹⁸(99-digit number)

18342423430913938750…42815170848093405189

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.834 × 10⁹⁸(99-digit number)

18342423430913938750…42815170848093405191

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

3.668 × 10⁹⁸(99-digit number)

36684846861827877501…85630341696186810379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.668 × 10⁹⁸(99-digit number)

36684846861827877501…85630341696186810381

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

7.336 × 10⁹⁸(99-digit number)

73369693723655755002…71260683392373620759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.336 × 10⁹⁸(99-digit number)

73369693723655755002…71260683392373620761

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

1.467 × 10⁹⁹(100-digit number)

14673938744731151000…42521366784747241519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.467 × 10⁹⁹(100-digit number)

14673938744731151000…42521366784747241521

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

2.934 × 10⁹⁹(100-digit number)

29347877489462302001…85042733569494483039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.934 × 10⁹⁹(100-digit number)

29347877489462302001…85042733569494483041

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