Block #922,325

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 9:36:10 AM · Difficulty 10.9156 · 5,887,380 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e1ad65131b8f4e782e20de4fc68f816e6b1b8797a7c02b4098d3ff2c0aebe7ab

View on Chainz ↗

Height

#922,325

Difficulty

10.915583

Transactions

Size

115.98 KB

Version

Bits

0aea639e

Nonce

293,973,236

Timestamp

2/4/2015, 9:36:10 AM

Confirmations

5,887,380

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5e95b5e4f4b0f43a77bb534bfb63ea701acc8746278a3df3c4c29d94815a7314

Transactions (5)

Coinbase57963dd2d79a0a…a4a150b94075d6

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

810b8f7573dd16…3c4a2a7129e648

200 in → 1 out1145.1317 XPM28.96 KB

AKuP4XsJ…owbodNxQ

9ef83fc5456d43…f53ded235204d3

200 in → 1 out911.6001 XPM28.92 KB

AKuP4XsJ…owbodNxQ

4a2194591f467d…c014cee67cd76e

200 in → 1 out987.9859 XPM28.95 KB

AKuP4XsJ…owbodNxQ

fb897f728b2f47…c05b782620c1ee

200 in → 1 out1007.9616 XPM28.95 KB

AKuP4XsJ…owbodNxQ

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.

6.146 × 10⁹⁵(96-digit number)

61461920741408293450…67030314388057122879

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

6.146 × 10⁹⁵(96-digit number)

61461920741408293450…67030314388057122879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.146 × 10⁹⁵(96-digit number)

61461920741408293450…67030314388057122881

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

1.229 × 10⁹⁶(97-digit number)

12292384148281658690…34060628776114245759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.229 × 10⁹⁶(97-digit number)

12292384148281658690…34060628776114245761

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

2.458 × 10⁹⁶(97-digit number)

24584768296563317380…68121257552228491519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.458 × 10⁹⁶(97-digit number)

24584768296563317380…68121257552228491521

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

4.916 × 10⁹⁶(97-digit number)

49169536593126634760…36242515104456983039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.916 × 10⁹⁶(97-digit number)

49169536593126634760…36242515104456983041

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

9.833 × 10⁹⁶(97-digit number)

98339073186253269520…72485030208913966079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.833 × 10⁹⁶(97-digit number)

98339073186253269520…72485030208913966081

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 #922,325

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