Block #922,490

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2015, 12:44:57 PM · Difficulty 10.9152 · 5,870,042 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e40c2e2856ced0ff60f6e11156f10fb2b12c774201825fae22d44e79e5f0750

View on Chainz ↗

Height

#922,490

Difficulty

10.915209

Transactions

Size

116.07 KB

Version

Bits

0aea4b24

Nonce

754,540,298

Timestamp

2/4/2015, 12:44:57 PM

Confirmations

5,870,042

Merkle Root

9f9ea01d0454bd0be1cdbef6d01f03f4c38eff4bf267f183c15fc4b0729e7963

Transactions (5)

Coinbase53b0a217033a1e…517a5f55f25554

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

7df3be6d48133e…469599e66e3d17

200 in → 1 out1027.0197 XPM28.97 KB

AKuP4XsJ…owbodNxQ

8aa4dbfa49c95d…e3619b9c20fe82

200 in → 1 out944.1837 XPM28.96 KB

AKuP4XsJ…owbodNxQ

0a74e281f057fc…f80e38e6ce95ce

200 in → 1 out1075.8305 XPM28.96 KB

AKuP4XsJ…owbodNxQ

edc18fbec656ef…80d4ffcc379259

200 in → 1 out907.7314 XPM28.96 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.

3.209 × 10⁹⁹(100-digit number)

32093892106064840154…56857973557467545599

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

3.209 × 10⁹⁹(100-digit number)

32093892106064840154…56857973557467545599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.209 × 10⁹⁹(100-digit number)

32093892106064840154…56857973557467545601

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

6.418 × 10⁹⁹(100-digit number)

64187784212129680309…13715947114935091199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.418 × 10⁹⁹(100-digit number)

64187784212129680309…13715947114935091201

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

1.283 × 10¹⁰⁰(101-digit number)

12837556842425936061…27431894229870182399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.283 × 10¹⁰⁰(101-digit number)

12837556842425936061…27431894229870182401

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

2.567 × 10¹⁰⁰(101-digit number)

25675113684851872123…54863788459740364799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.567 × 10¹⁰⁰(101-digit number)

25675113684851872123…54863788459740364801

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

5.135 × 10¹⁰⁰(101-digit number)

51350227369703744247…09727576919480729599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.135 × 10¹⁰⁰(101-digit number)

51350227369703744247…09727576919480729601

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