Block #569,922

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/31/2014, 11:45:29 AM · Difficulty 10.9647 · 6,256,222 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

be4a611a323237ed957ddcf7d0d7d9d9afd138f5cd2c250e7ebfb06ddaaf5ed4

View on Chainz ↗

Height

#569,922

Difficulty

10.964717

Transactions

Size

1.27 KB

Version

Bits

0af6f7b8

Nonce

72,958,253

Timestamp

5/31/2014, 11:45:29 AM

Confirmations

6,256,222

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8e2751b93250431f859f8086444035975f4a16c5f4a1caf363f467e9ac9fd670

Transactions (4)

Coinbase571e16b1109e94…6225bbf42794a9

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

69a6ec1636e6bb…6bdc0192150402

2 in → 1 out859.9900 XPM342 B

Aa4tZEMs…xjqWUths

65cc4e4d954313…ba18fd9acb2747

3 in → 2 out4.2427 XPM523 B

AHV61zih…SaAmRxM6 Aez7JGBv…zQSw1USt

94da84a9ed5d0a…4d1d34059e7f2e

1 in → 2 out7.2587 XPM225 B

AG8u7ddV…cU5QJSqk AS16oAL7…W9zKhPnE

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.

7.523 × 10⁹⁹(100-digit number)

75232327204329549011…35846106982245785599

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

7.523 × 10⁹⁹(100-digit number)

75232327204329549011…35846106982245785599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.523 × 10⁹⁹(100-digit number)

75232327204329549011…35846106982245785601

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

1.504 × 10¹⁰⁰(101-digit number)

15046465440865909802…71692213964491571199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.504 × 10¹⁰⁰(101-digit number)

15046465440865909802…71692213964491571201

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

3.009 × 10¹⁰⁰(101-digit number)

30092930881731819604…43384427928983142399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.009 × 10¹⁰⁰(101-digit number)

30092930881731819604…43384427928983142401

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

6.018 × 10¹⁰⁰(101-digit number)

60185861763463639209…86768855857966284799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.018 × 10¹⁰⁰(101-digit number)

60185861763463639209…86768855857966284801

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

1.203 × 10¹⁰¹(102-digit number)

12037172352692727841…73537711715932569599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.203 × 10¹⁰¹(102-digit number)

12037172352692727841…73537711715932569601

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 #569,922

Cookie Preferences