Block #440,308

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 8:33:29 AM · Difficulty 10.3504 · 6,362,384 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d23428e1713bd1594df499edff40c2c5a8caa1b69c6c4a5ac3d2f9e20c180d45

View on Chainz ↗

Height

#440,308

Difficulty

10.350425

Transactions

Size

1.86 KB

Version

Bits

0a59b574

Nonce

84,038

Timestamp

3/12/2014, 8:33:29 AM

Confirmations

6,362,384

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

bf9d7aa1f1c3fb622ddc41e6564450408a2c7c6a498eb866a46aabe623be693d

Transactions (2)

Coinbasef8d01421f7672a…e859e66d047459

1 in → 23 out9.3200 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

f8c5418d76715b…9ee78934d296d4

6 in → 2 out6.4372 XPM966 B

AbPXfccS…4F7crkyw AFub27uN…X6nMP2pT

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.

1.466 × 10⁹³(94-digit number)

14660238073215155321…48695505138889548159

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

1.466 × 10⁹³(94-digit number)

14660238073215155321…48695505138889548159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.466 × 10⁹³(94-digit number)

14660238073215155321…48695505138889548161

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

2.932 × 10⁹³(94-digit number)

29320476146430310643…97391010277779096319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.932 × 10⁹³(94-digit number)

29320476146430310643…97391010277779096321

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

5.864 × 10⁹³(94-digit number)

58640952292860621286…94782020555558192639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.864 × 10⁹³(94-digit number)

58640952292860621286…94782020555558192641

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

1.172 × 10⁹⁴(95-digit number)

11728190458572124257…89564041111116385279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.172 × 10⁹⁴(95-digit number)

11728190458572124257…89564041111116385281

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

2.345 × 10⁹⁴(95-digit number)

23456380917144248514…79128082222232770559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.345 × 10⁹⁴(95-digit number)

23456380917144248514…79128082222232770561

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