Block #698,933

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/29/2014, 10:13:23 PM · Difficulty 10.9591 · 6,118,345 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

696233c0d193ed8325f20b5cc7aeaeff1516ed1823ec04b6ee694a0fb7177c09

View on Chainz ↗

Height

#698,933

Difficulty

10.959125

Transactions

Size

885 B

Version

Bits

0af5893b

Nonce

1,571,047,745

Timestamp

8/29/2014, 10:13:23 PM

Confirmations

6,118,345

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

763e060943d74b761036c96e6076536aeb21692427a53e27fe04621f11a80d87

Transactions (4)

Coinbase8eeaf63d0e1b9e…8aeafdf661e35a

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

9a0cea0fa7aea6…cc7a7e77771eb9

1 in → 2 out8.3000 XPM226 B

Abs1CTRR…uk6ieBYF AM2cjR3D…2McHdUUH

3aa474826d2adb…b65132452c8320

1 in → 2 out8.3000 XPM226 B

AYU1Ynxb…6LNs2ZYM ARXjJrLh…oiTiqdCi

cd7adbb5b74065…3f969d4a8c24ec

1 in → 2 out8.3000 XPM226 B

ANF8gAYZ…6J4KfsRz APVdfbfH…1FUmTWCf

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.

1.166 × 10⁹⁸(99-digit number)

11666444266863836695…17306225566846049279

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

1.166 × 10⁹⁸(99-digit number)

11666444266863836695…17306225566846049279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.166 × 10⁹⁸(99-digit number)

11666444266863836695…17306225566846049281

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

2.333 × 10⁹⁸(99-digit number)

23332888533727673390…34612451133692098559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.333 × 10⁹⁸(99-digit number)

23332888533727673390…34612451133692098561

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

4.666 × 10⁹⁸(99-digit number)

46665777067455346781…69224902267384197119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.666 × 10⁹⁸(99-digit number)

46665777067455346781…69224902267384197121

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

9.333 × 10⁹⁸(99-digit number)

93331554134910693562…38449804534768394239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.333 × 10⁹⁸(99-digit number)

93331554134910693562…38449804534768394241

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

1.866 × 10⁹⁹(100-digit number)

18666310826982138712…76899609069536788479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.866 × 10⁹⁹(100-digit number)

18666310826982138712…76899609069536788481

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 #698,933

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