Block #389,823

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2014, 6:02:36 PM · Difficulty 10.4221 · 6,413,351 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

030320ddaafba3470e261b41c80744e2ec0588ead41f7d02f10cf55788a75d4b

View on Chainz ↗

Height

#389,823

Difficulty

10.422116

Transactions

Size

1.58 KB

Version

Bits

0a6c0fc6

Nonce

138,459

Timestamp

2/4/2014, 6:02:36 PM

Confirmations

6,413,351

Mined by

⛏️ aR+aAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

6530fe6fa7c9a77f29c6aa3f870f483277d7d73fc1f7512e6da1feab3c72ad8b

Transactions (4)

Coinbaseaf8f086ec494d5…26722c44d1e1a8

1 in → 23 out9.1900 XPM845 B

AQvZBsUo…hppgRZTJ AGPYJBwg…5yWMRKmU Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

116e996a30ef40…0f4847c7b487a5

1 in → 2 out5.1322 XPM226 B

AKvyLahD…qr57yRqc AMGWQxaG…LZq89wAX

df5668b7c4e5e6…0a9afac38268b7

1 in → 2 out2.1175 XPM225 B

ANszK4UD…7EFTLUyi AKLMM364…P8XaoQFw

a0f0e767c6850b…7df7f1ec206cb0

1 in → 2 out4.2437 XPM227 B

AHfF98wE…6XjKCBq9 AKsdUUNS…5oKwHt5W

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.

6.499 × 10⁹⁸(99-digit number)

64997304770120467151…72013988621613465599

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

6.499 × 10⁹⁸(99-digit number)

64997304770120467151…72013988621613465599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.499 × 10⁹⁸(99-digit number)

64997304770120467151…72013988621613465601

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

1.299 × 10⁹⁹(100-digit number)

12999460954024093430…44027977243226931199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.299 × 10⁹⁹(100-digit number)

12999460954024093430…44027977243226931201

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

2.599 × 10⁹⁹(100-digit number)

25998921908048186860…88055954486453862399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.599 × 10⁹⁹(100-digit number)

25998921908048186860…88055954486453862401

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

5.199 × 10⁹⁹(100-digit number)

51997843816096373721…76111908972907724799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.199 × 10⁹⁹(100-digit number)

51997843816096373721…76111908972907724801

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

1.039 × 10¹⁰⁰(101-digit number)

10399568763219274744…52223817945815449599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.039 × 10¹⁰⁰(101-digit number)

10399568763219274744…52223817945815449601

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