Block #1,404,579

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/8/2016, 3:16:52 PM · Difficulty 10.8054 · 5,434,667 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e98f7b1bb4df6f73f9141566e636394cbddbf55cdefe3113b8b0c34594fdbfad

View on Chainz ↗

Height

#1,404,579

Difficulty

10.805449

Transactions

Size

870 B

Version

Bits

0ace31ec

Nonce

771,431,085

Timestamp

1/8/2016, 3:16:52 PM

Confirmations

5,434,667

Mined by

⛏️ P2SHAK6Nve2KBzXAJ7Ru1ZZ1JrLLrRBtP4pnfq

Merkle Root

2e22823f035bf64dd0f2b1faa6554a15effb7240a17b2c40af908685c451705e

Transactions (2)

Coinbase7d16ad45ad4cbf…7e40ede9b3b4a5

1 in → 1 out8.5600 XPM110 B

AK6Nve2K…BtP4pnfq

e1c2f7376739a6…73eee654748908

4 in → 2 out1211.7249 XPM671 B

AVpJbiVd…f3No8Y5f Aayd1JPL…FTHVH8Xg

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.

1.366 × 10⁹³(94-digit number)

13662789496048435518…90750840327580407999

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

1.366 × 10⁹³(94-digit number)

13662789496048435518…90750840327580407999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.366 × 10⁹³(94-digit number)

13662789496048435518…90750840327580408001

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

2.732 × 10⁹³(94-digit number)

27325578992096871037…81501680655160815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.732 × 10⁹³(94-digit number)

27325578992096871037…81501680655160816001

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

5.465 × 10⁹³(94-digit number)

54651157984193742075…63003361310321631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.465 × 10⁹³(94-digit number)

54651157984193742075…63003361310321632001

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

1.093 × 10⁹⁴(95-digit number)

10930231596838748415…26006722620643263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.093 × 10⁹⁴(95-digit number)

10930231596838748415…26006722620643264001

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

2.186 × 10⁹⁴(95-digit number)

21860463193677496830…52013445241286527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.186 × 10⁹⁴(95-digit number)

21860463193677496830…52013445241286528001

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 #1,404,579

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