Block #508,120

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/24/2014, 4:41:43 AM · Difficulty 10.8175 · 6,286,670 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

05ab9145cd8850a4726685346dc2b1a7103dc30110bd5553284f5a27813904c9

View on Chainz ↗

Height

#508,120

Difficulty

10.817525

Transactions

Size

894 B

Version

Bits

0ad14952

Nonce

6,250,392

Timestamp

4/24/2014, 4:41:43 AM

Confirmations

6,286,670

Mined by

⛏️ P2SHAH7bMCXByACu8HbWjGsysjnSppGDKjCWLY

Merkle Root

f9d137fd114ca442eeb6d63458d4f31333c91f9e2a862f2deca18cd21ba53d8a

Transactions (4)

Coinbase85ba0dd43718ba…1cf96b5a69d2fd

1 in → 1 out8.5600 XPM111 B

AH7bMCXB…GDKjCWLY

5862c510a90d73…3be67c19cfb7a0

2 in → 2 out17.2600 XPM307 B

ATx8iQ8h…XbxyuQRB AJRHQ5VN…dM5NqY6h

fac5cf9e866789…83bad0f0c77d2d

1 in → 1 out2.9907 XPM191 B

AZbVGqSq…g6UpEL8v

b1b2530c9a8c16…ef0eb44ffbd5ee

1 in → 1 out0.3354 XPM193 B

AGXFqSyj…FxquNuxH

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.

9.055 × 10⁹⁸(99-digit number)

90556927056849914092…32290761190879625599

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

9.055 × 10⁹⁸(99-digit number)

90556927056849914092…32290761190879625599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.055 × 10⁹⁸(99-digit number)

90556927056849914092…32290761190879625601

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

1.811 × 10⁹⁹(100-digit number)

18111385411369982818…64581522381759251199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.811 × 10⁹⁹(100-digit number)

18111385411369982818…64581522381759251201

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

3.622 × 10⁹⁹(100-digit number)

36222770822739965636…29163044763518502399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.622 × 10⁹⁹(100-digit number)

36222770822739965636…29163044763518502401

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

7.244 × 10⁹⁹(100-digit number)

72445541645479931273…58326089527037004799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.244 × 10⁹⁹(100-digit number)

72445541645479931273…58326089527037004801

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

1.448 × 10¹⁰⁰(101-digit number)

14489108329095986254…16652179054074009599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.448 × 10¹⁰⁰(101-digit number)

14489108329095986254…16652179054074009601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.897 × 10¹⁰⁰(101-digit number)

28978216658191972509…33304358108148019199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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