Block #402,729

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2014, 3:25:32 PM · Difficulty 10.4382 · 6,407,167 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fdc4ea46f8d149b699041bbb261ee238edd2b0447c9b7ffc997c73ab7fef7a7b

View on Chainz ↗

Height

#402,729

Difficulty

10.438153

Transactions

Size

969 B

Version

Bits

0a702acb

Nonce

17,384

Timestamp

2/13/2014, 3:25:32 PM

Confirmations

6,407,167

Mined by

⛏️ %aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

12bdc5cd39875880387678aaf43724f977420987e14fe1ea057f74bd3b54ed46

Transactions (1)

Coinbase12bdc5cd398758…7f74bd3b54ed46

1 in → 24 out9.1600 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYRvXuTr…CkbwFeLY AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH

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.

1.785 × 10⁹⁴(95-digit number)

17855381605920470974…95759605871435265999

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

1.785 × 10⁹⁴(95-digit number)

17855381605920470974…95759605871435265999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.785 × 10⁹⁴(95-digit number)

17855381605920470974…95759605871435266001

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

3.571 × 10⁹⁴(95-digit number)

35710763211840941948…91519211742870531999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.571 × 10⁹⁴(95-digit number)

35710763211840941948…91519211742870532001

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

7.142 × 10⁹⁴(95-digit number)

71421526423681883897…83038423485741063999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.142 × 10⁹⁴(95-digit number)

71421526423681883897…83038423485741064001

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

1.428 × 10⁹⁵(96-digit number)

14284305284736376779…66076846971482127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.428 × 10⁹⁵(96-digit number)

14284305284736376779…66076846971482128001

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

2.856 × 10⁹⁵(96-digit number)

28568610569472753559…32153693942964255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.856 × 10⁹⁵(96-digit number)

28568610569472753559…32153693942964256001

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 #402,729

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