Block #922,393

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 10:49:48 AM · Difficulty 10.9155 · 5,888,737 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f4976afc19f177058e9baa7cae3a502efea29656119b23c0063e53caa57c6da5

View on Chainz ↗

Height

#922,393

Difficulty

10.915485

Transactions

Size

115.99 KB

Version

Bits

0aea5d35

Nonce

1,253,350,915

Timestamp

2/4/2015, 10:49:48 AM

Confirmations

5,888,737

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cbedd127ee4fde49e9bca0da899ea2b72a119525b71b447750a7a199cabb33a8

Transactions (5)

Coinbase86ecb369c94b03…bf1d204be383e3

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

0a428ef4f09193…50623991d27734

200 in → 1 out1098.6657 XPM28.95 KB

AKuP4XsJ…owbodNxQ

94a1bea7930412…6b881949ce1596

200 in → 1 out1105.4914 XPM28.94 KB

AKuP4XsJ…owbodNxQ

c52634c18fd811…f0847d04637993

200 in → 1 out971.9245 XPM28.95 KB

AKuP4XsJ…owbodNxQ

7b55001c4ca331…aad79017a6c664

200 in → 1 out988.0584 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.

6.235 × 10⁹⁷(98-digit number)

62350373463848423645…63575185794375086079

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

6.235 × 10⁹⁷(98-digit number)

62350373463848423645…63575185794375086079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.235 × 10⁹⁷(98-digit number)

62350373463848423645…63575185794375086081

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

1.247 × 10⁹⁸(99-digit number)

12470074692769684729…27150371588750172159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.247 × 10⁹⁸(99-digit number)

12470074692769684729…27150371588750172161

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

2.494 × 10⁹⁸(99-digit number)

24940149385539369458…54300743177500344319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.494 × 10⁹⁸(99-digit number)

24940149385539369458…54300743177500344321

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

4.988 × 10⁹⁸(99-digit number)

49880298771078738916…08601486355000688639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.988 × 10⁹⁸(99-digit number)

49880298771078738916…08601486355000688641

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

9.976 × 10⁹⁸(99-digit number)

99760597542157477833…17202972710001377279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.976 × 10⁹⁸(99-digit number)

99760597542157477833…17202972710001377281

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 #922,393

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