Block #1,739,779

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/29/2016, 7:42:18 PM · Difficulty 10.7216 · 5,087,331 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a749b7117459a9ebce59750444b47c014d59342d9da74c63ca0f74c4fb781d75

View on Chainz ↗

Height

#1,739,779

Difficulty

10.721563

Transactions

Size

4.32 KB

Version

Bits

0ab8b85f

Nonce

453,907,742

Timestamp

8/29/2016, 7:42:18 PM

Confirmations

5,087,331

Mined by

⛏️ P2SHAe7ZDix5jSJpCPJjUiVQnAVwNmVjZN993D

Merkle Root

184d17d81da36fb66ae9f2c2f453f871d49dc6cd49a0338f30d3a69faebbd177

Transactions (3)

Coinbasea82e2b80dd6c4f…922fe23d690402

1 in → 1 out8.7400 XPM109 B

Ae7ZDix5…VjZN993D

e84d6d4246792c…cf7fffa9b2a687

4 in → 51 out13.9936 XPM2.28 KB

AHuRgVyA…3HRzvHj6 AbWFv1Kg…bddJVNnX AaeL1bhm…yB1BpmVR AHJEQXvi…ofxfmKDm AJXC16dP…shBAMWUD

fd6b1dc05c4061…743473e7f9f5ce

1 in → 51 out1.8800 XPM1.85 KB

ANWc4squ…uDinN1kN AMEjBhbJ…gxpuzXby ANWvYEBp…zn3atQvK AQ1P7RaB…SWu1AFS7 ANiTFZMA…ufBYqC23

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.

5.466 × 10⁹⁴(95-digit number)

54663733643529670731…33795666986227036159

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

5.466 × 10⁹⁴(95-digit number)

54663733643529670731…33795666986227036159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.466 × 10⁹⁴(95-digit number)

54663733643529670731…33795666986227036161

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

1.093 × 10⁹⁵(96-digit number)

10932746728705934146…67591333972454072319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.093 × 10⁹⁵(96-digit number)

10932746728705934146…67591333972454072321

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

2.186 × 10⁹⁵(96-digit number)

21865493457411868292…35182667944908144639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.186 × 10⁹⁵(96-digit number)

21865493457411868292…35182667944908144641

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

4.373 × 10⁹⁵(96-digit number)

43730986914823736584…70365335889816289279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.373 × 10⁹⁵(96-digit number)

43730986914823736584…70365335889816289281

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

8.746 × 10⁹⁵(96-digit number)

87461973829647473169…40730671779632578559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.746 × 10⁹⁵(96-digit number)

87461973829647473169…40730671779632578561

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 #1,739,779

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