Block #1,399,124

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/4/2016, 7:34:58 PM · Difficulty 10.8070 · 5,417,884 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bdb66bd5b04c16b5ee06a50fe58798aae0a4647446fb0b497f30c9315bbedd44

View on Chainz ↗

Height

#1,399,124

Difficulty

10.806967

Transactions

Size

4.16 KB

Version

Bits

0ace9562

Nonce

1,154,566,150

Timestamp

1/4/2016, 7:34:58 PM

Confirmations

5,417,884

Mined by

⛏️ P2SHAZv44aCMrfdUqp7FGTEozqXg3cSQbFCG6X

Merkle Root

d1308e8eb8700e76144bd91a4532487cefd52b89a63f95d666772e30b352f6cd

Transactions (3)

Coinbase7623b58ecbc4f6…8360696d48bdce

1 in → 1 out8.6000 XPM110 B

AZv44aCM…SQbFCG6X

ced1d51e429421…6e3b42345da100

1 in → 46 out27.6591 XPM1.68 KB

ASG21nzq…iMYaGLq3 ALvPZTWS…S9MGQgrc AMLcJVyP…UMPoLhHE AeAgDyTn…8uKNgvMR AKMjKLuH…ajPQfnyf

b5fa5a3e0f4ede…b0f07cb9145069

4 in → 51 out5.6174 XPM2.28 KB

ATkiCeum…91r8eHmY AKsSBvGX…wzCKCnbZ ATQ2RfSs…yao2HZMj AUYnBpY4…rpRqkZQC AGxg8aKK…AbBR9dJY

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.

7.048 × 10⁹⁴(95-digit number)

70486841900846151753…35458177402809524639

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

7.048 × 10⁹⁴(95-digit number)

70486841900846151753…35458177402809524639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.048 × 10⁹⁴(95-digit number)

70486841900846151753…35458177402809524641

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

1.409 × 10⁹⁵(96-digit number)

14097368380169230350…70916354805619049279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.409 × 10⁹⁵(96-digit number)

14097368380169230350…70916354805619049281

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

2.819 × 10⁹⁵(96-digit number)

28194736760338460701…41832709611238098559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.819 × 10⁹⁵(96-digit number)

28194736760338460701…41832709611238098561

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

5.638 × 10⁹⁵(96-digit number)

56389473520676921402…83665419222476197119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.638 × 10⁹⁵(96-digit number)

56389473520676921402…83665419222476197121

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

1.127 × 10⁹⁶(97-digit number)

11277894704135384280…67330838444952394239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.127 × 10⁹⁶(97-digit number)

11277894704135384280…67330838444952394241

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 #1,399,124

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