Block #527,699

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/6/2014, 5:26:51 AM · Difficulty 10.8842 · 6,275,615 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4e3433aa69a16f1d691575eb47a033aa4a696134bb74de07ade3464cf85fd22b

View on Chainz ↗

Height

#527,699

Difficulty

10.884154

Transactions

Size

1.34 KB

Version

Bits

0ae257f1

Nonce

80,018

Timestamp

5/6/2014, 5:26:51 AM

Confirmations

6,275,615

Mined by

⛏️ SAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ee1d12a5f6bb6d96dc541436564867779ec480531ff0fbd23540a6826231cbc9

Transactions (4)

Coinbasee2fc1015ed403a…1e475a9a621251

1 in → 17 out8.4300 XPM641 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 ANNg88pG…ppn21sTe AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j

cd047e4fc6f87c…791461b2b6dda4

1 in → 2 out8.4500 XPM193 B

AXDEZh15…FbrAPGkC AeKNrjNj…1NEq95Ta

ae87ef48eaf015…4ccf86501a0eeb

1 in → 2 out87.8838 XPM227 B

Aa5KSvSy…DCwz8TMP AW2WF5Aa…Vi1LVcBG

7bbecf2bc77bbe…716b9be77aa85e

1 in → 2 out78.6802 XPM226 B

AK3JUq3A…QotRAkhT AGdWVjRk…LFVsqCnK

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.

5.631 × 10⁹⁴(95-digit number)

56310472844864202443…81629702657788093699

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

5.631 × 10⁹⁴(95-digit number)

56310472844864202443…81629702657788093699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.631 × 10⁹⁴(95-digit number)

56310472844864202443…81629702657788093701

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

1.126 × 10⁹⁵(96-digit number)

11262094568972840488…63259405315576187399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.126 × 10⁹⁵(96-digit number)

11262094568972840488…63259405315576187401

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

2.252 × 10⁹⁵(96-digit number)

22524189137945680977…26518810631152374799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.252 × 10⁹⁵(96-digit number)

22524189137945680977…26518810631152374801

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

4.504 × 10⁹⁵(96-digit number)

45048378275891361954…53037621262304749599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.504 × 10⁹⁵(96-digit number)

45048378275891361954…53037621262304749601

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

9.009 × 10⁹⁵(96-digit number)

90096756551782723909…06075242524609499199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.009 × 10⁹⁵(96-digit number)

90096756551782723909…06075242524609499201

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