Block #1,073,814

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/24/2015, 3:28:21 PM · Difficulty 10.7414 · 5,768,489 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67f8342955b91a92362c815783d9476b31906f115c9fa915d301d374f6426ce6

View on Chainz ↗

Height

#1,073,814

Difficulty

10.741381

Transactions

Size

111.81 KB

Version

Bits

0abdcb24

Nonce

234,149,584

Timestamp

5/24/2015, 3:28:21 PM

Confirmations

5,768,489

Mined by

⛏️ P2SHAJBNdhqYqhVHBJXbL9Up62UPZ9v96mgNnu

Merkle Root

25471b6e6a8f9a9cd8407f698c02a03b2968679d45b2e590575aa464d3bfbd56

Transactions (4)

Coinbase8304f8a4bfce5c…4a5978198dd8bf

1 in → 1 out9.8100 XPM109 B

AJBNdhqY…v96mgNnu

4d64cb7caeaca4…8a7aac887ebfc0

17 in → 2 out681.8187 XPM2.53 KB

AYeGLxtJ…3XFCDFMm AaRoemN6…T4vkVeNX

cb5e19d0f589c6…7ca29a14b33b03

502 in → 2 out2000.0000 XPM72.62 KB

AJJ2jGa9…dqLGp1ir ATJeka45…7yXJQkRn

76efcc153e6685…6cc6c2921e8dc7

252 in → 1 out999.9900 XPM36.46 KB

AJda9EXJ…YUyCPsdc

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.

2.414 × 10⁹⁴(95-digit number)

24147680308064667743…13423620526533424439

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

2.414 × 10⁹⁴(95-digit number)

24147680308064667743…13423620526533424439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.414 × 10⁹⁴(95-digit number)

24147680308064667743…13423620526533424441

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

4.829 × 10⁹⁴(95-digit number)

48295360616129335487…26847241053066848879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.829 × 10⁹⁴(95-digit number)

48295360616129335487…26847241053066848881

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

9.659 × 10⁹⁴(95-digit number)

96590721232258670975…53694482106133697759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.659 × 10⁹⁴(95-digit number)

96590721232258670975…53694482106133697761

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

1.931 × 10⁹⁵(96-digit number)

19318144246451734195…07388964212267395519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.931 × 10⁹⁵(96-digit number)

19318144246451734195…07388964212267395521

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

3.863 × 10⁹⁵(96-digit number)

38636288492903468390…14777928424534791039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.863 × 10⁹⁵(96-digit number)

38636288492903468390…14777928424534791041

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 #1,073,814

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