Block #1,694,240

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/29/2016, 3:47:39 PM · Difficulty 10.6807 · 5,132,834 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43642b80256038bdff5308383c2b3003b8dd773a534103edfb980047dea6bd70

View on Chainz ↗

Height

#1,694,240

Difficulty

10.680695

Transactions

Size

6.50 KB

Version

Bits

0aae4209

Nonce

881,928,769

Timestamp

7/29/2016, 3:47:39 PM

Confirmations

5,132,834

Mined by

⛏️ P2SHAf7PydF3o4mGUQdbwRnfvtCu4Un7pAHFSe

Merkle Root

2fee9e2e07f465539d7a1fa9a6b449caa52067ca6f5c04504d6ef8ab999b0448

Transactions (2)

Coinbase63e51a7e5e862a…fa1636448069de

1 in → 1 out8.8200 XPM110 B

Af7PydF3…n7pAHFSe

a93805461e3468…65c08eebd1a69f

43 in → 2 out267.6476 XPM6.30 KB

AVoP8KR5…BKqrw4Zb AQdYofSx…XYLNUQXA

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.

2.371 × 10⁹⁸(99-digit number)

23713370915038535934…83831809372731473919

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

2.371 × 10⁹⁸(99-digit number)

23713370915038535934…83831809372731473919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.371 × 10⁹⁸(99-digit number)

23713370915038535934…83831809372731473921

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

4.742 × 10⁹⁸(99-digit number)

47426741830077071868…67663618745462947839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.742 × 10⁹⁸(99-digit number)

47426741830077071868…67663618745462947841

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

9.485 × 10⁹⁸(99-digit number)

94853483660154143737…35327237490925895679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.485 × 10⁹⁸(99-digit number)

94853483660154143737…35327237490925895681

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

1.897 × 10⁹⁹(100-digit number)

18970696732030828747…70654474981851791359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.897 × 10⁹⁹(100-digit number)

18970696732030828747…70654474981851791361

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

3.794 × 10⁹⁹(100-digit number)

37941393464061657495…41308949963703582719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.794 × 10⁹⁹(100-digit number)

37941393464061657495…41308949963703582721

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 #1,694,240

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