Block #400,148

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 9:05:13 PM · Difficulty 10.4329 · 6,410,734 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

87e119b638a54f681c462092f95f2c62b3c07b2bd6bfeb5e89d82d6f793a11b4

View on Chainz ↗

Height

#400,148

Difficulty

10.432877

Transactions

Size

967 B

Version

Bits

0a6ed107

Nonce

21,039

Timestamp

2/11/2014, 9:05:13 PM

Confirmations

6,410,734

Mined by

⛏️ aRiAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

4105b344229fd80cd2e1ff72f30e418f00dab3ffca065a0a7ebe777436a38919

Transactions (1)

Coinbase4105b344229fd8…be777436a38919

1 in → 24 out9.1700 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AZemWJAo…6jhDtieG Ae58nAEb…GFUA15fv

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.

5.349 × 10⁹⁰(91-digit number)

53491460666711670881…58855371729098819609

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

5.349 × 10⁹⁰(91-digit number)

53491460666711670881…58855371729098819609

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.349 × 10⁹⁰(91-digit number)

53491460666711670881…58855371729098819611

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

1.069 × 10⁹¹(92-digit number)

10698292133342334176…17710743458197639219

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.069 × 10⁹¹(92-digit number)

10698292133342334176…17710743458197639221

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

2.139 × 10⁹¹(92-digit number)

21396584266684668352…35421486916395278439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.139 × 10⁹¹(92-digit number)

21396584266684668352…35421486916395278441

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

4.279 × 10⁹¹(92-digit number)

42793168533369336705…70842973832790556879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.279 × 10⁹¹(92-digit number)

42793168533369336705…70842973832790556881

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

8.558 × 10⁹¹(92-digit number)

85586337066738673410…41685947665581113759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.558 × 10⁹¹(92-digit number)

85586337066738673410…41685947665581113761

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 #400,148

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