Block #506,948

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2014, 9:55:26 AM · Difficulty 10.8158 · 6,309,081 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

621c0d75f29008e9f7a90ecbcdbb3f1b8146217c5d3d21183a3d4ca43bba9cb9

View on Chainz ↗

Height

#506,948

Difficulty

10.815789

Transactions

Size

208 B

Version

Bits

0ad0d791

Nonce

180,047,932

Timestamp

4/23/2014, 9:55:26 AM

Confirmations

6,309,081

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

d781ec2e101ebd7caacb9a5c50f95b48d1d9bb53524dbf3f2fd53b3d717bf21c

Transactions (1)

Coinbased781ec2e101ebd…d53b3d717bf21c

1 in → 1 out8.5300 XPM116 B

AbwWkWZt…kawDhufa

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.

1.726 × 10⁹⁹(100-digit number)

17265627242558196261…53499044792432312799

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

1.726 × 10⁹⁹(100-digit number)

17265627242558196261…53499044792432312799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.726 × 10⁹⁹(100-digit number)

17265627242558196261…53499044792432312801

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

3.453 × 10⁹⁹(100-digit number)

34531254485116392523…06998089584864625599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.453 × 10⁹⁹(100-digit number)

34531254485116392523…06998089584864625601

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

6.906 × 10⁹⁹(100-digit number)

69062508970232785046…13996179169729251199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.906 × 10⁹⁹(100-digit number)

69062508970232785046…13996179169729251201

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

1.381 × 10¹⁰⁰(101-digit number)

13812501794046557009…27992358339458502399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.381 × 10¹⁰⁰(101-digit number)

13812501794046557009…27992358339458502401

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

2.762 × 10¹⁰⁰(101-digit number)

27625003588093114018…55984716678917004799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.762 × 10¹⁰⁰(101-digit number)

27625003588093114018…55984716678917004801

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 #506,948

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