Block #529,159

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/7/2014, 2:15:26 AM · Difficulty 10.8889 · 6,274,182 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea683c90a71684daad6ba20d6ef785e0eb95053194d0f116ec927f6e810754a1

View on Chainz ↗

Height

#529,159

Difficulty

10.888932

Transactions

Size

2.45 KB

Version

Bits

0ae39111

Nonce

4,974,108

Timestamp

5/7/2014, 2:15:26 AM

Confirmations

6,274,182

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3d4cb07754b052937be2ccfcd395d84fd4bf0451f3057d6a68cbf1d666c549ae

Transactions (4)

Coinbase06b97c08d7b6cd…f6ba164ca120e7

1 in → 1 out8.4600 XPM116 B

ANSXnLY2…Sd25TjkD

299221696b9581…3af18cef280fb4

1 in → 3 out8.4600 XPM226 B

AeKNrjNj…1NEq95Ta AMWb1h9q…GGwLTtwY ALHh4KEC…iRJuWFy8

f71c0e76e0f83e…2aee2a3124dc6c

12 in → 2 out55.1171 XPM1.81 KB

AU3Gezuy…C4CBgqp7 AeJT8ByC…AgotPjfS

8049b5938debac…c810b2f6ed8796

1 in → 2 out221.6894 XPM226 B

AM8GuxnN…AfjbhWoV ARrDW8vd…5CS18f2Z

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.

5.555 × 10⁹⁹(100-digit number)

55555177860438650395…37127703978666475199

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

5.555 × 10⁹⁹(100-digit number)

55555177860438650395…37127703978666475199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.555 × 10⁹⁹(100-digit number)

55555177860438650395…37127703978666475201

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

1.111 × 10¹⁰⁰(101-digit number)

11111035572087730079…74255407957332950399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.111 × 10¹⁰⁰(101-digit number)

11111035572087730079…74255407957332950401

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

2.222 × 10¹⁰⁰(101-digit number)

22222071144175460158…48510815914665900799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.222 × 10¹⁰⁰(101-digit number)

22222071144175460158…48510815914665900801

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

4.444 × 10¹⁰⁰(101-digit number)

44444142288350920316…97021631829331801599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.444 × 10¹⁰⁰(101-digit number)

44444142288350920316…97021631829331801601

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

8.888 × 10¹⁰⁰(101-digit number)

88888284576701840633…94043263658663603199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.888 × 10¹⁰⁰(101-digit number)

88888284576701840633…94043263658663603201

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