Block #531,134

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/8/2014, 7:47:18 AM · Difficulty 10.8934 · 6,264,039 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eee6509f03478e7b095f72c0f0da68b71bbc325432654d108cdf1792032ff298

View on Chainz ↗

Height

#531,134

Difficulty

10.893450

Transactions

Size

1.08 KB

Version

Bits

0ae4b921

Nonce

25,177,222

Timestamp

5/8/2014, 7:47:18 AM

Confirmations

6,264,039

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

59e1cb8d0c2cae3dfa3c17b3e84bcc85c4da89728b42d67b99af1caaca18b949

Transactions (5)

Coinbase970fd0224ee62f…eeb26f3915e462

1 in → 1 out8.4500 XPM116 B

ANSXnLY2…Sd25TjkD

b0fa4cf5a7aa15…2eb49f5c173474

1 in → 2 out7.7574 XPM226 B

AYcdD2Hi…wHqZ7q23 AUp1iRPn…z7tECCmP

c95aa882e0e66d…4c74e2d67f0793

1 in → 2 out2.8321 XPM225 B

AZZ5QsQX…AsWyVsdY AWQRGJ4e…egKZ6MjT

1f0e6097e522e2…521c50cdab70ce

1 in → 2 out7.2663 XPM226 B

AHaExXW4…YFhxHZNk APRDRkSC…SJksLRea

2dec844da952d9…8c915282c589cd

1 in → 2 out2.8938 XPM226 B

AKxrkk5S…8utaPXJJ 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.

2.334 × 10⁹⁹(100-digit number)

23341913921418680098…89269204872419867199

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

2.334 × 10⁹⁹(100-digit number)

23341913921418680098…89269204872419867199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.334 × 10⁹⁹(100-digit number)

23341913921418680098…89269204872419867201

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

4.668 × 10⁹⁹(100-digit number)

46683827842837360196…78538409744839734399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.668 × 10⁹⁹(100-digit number)

46683827842837360196…78538409744839734401

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

9.336 × 10⁹⁹(100-digit number)

93367655685674720392…57076819489679468799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.336 × 10⁹⁹(100-digit number)

93367655685674720392…57076819489679468801

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

1.867 × 10¹⁰⁰(101-digit number)

18673531137134944078…14153638979358937599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.867 × 10¹⁰⁰(101-digit number)

18673531137134944078…14153638979358937601

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

3.734 × 10¹⁰⁰(101-digit number)

37347062274269888156…28307277958717875199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.734 × 10¹⁰⁰(101-digit number)

37347062274269888156…28307277958717875201

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