Block #505,548

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/22/2014, 12:46:37 PM · Difficulty 10.8108 · 6,300,894 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c96e4848b9e99146a6d1057975e24631429fb4465aee61018b8acb5872eb1f5

View on Chainz ↗

Height

#505,548

Difficulty

10.810770

Transactions

Size

1.10 KB

Version

Bits

0acf8e9a

Nonce

330,062

Timestamp

4/22/2014, 12:46:37 PM

Confirmations

6,300,894

Mined by

⛏️ P2SHAQVsUPfQrRrT1Hf3D8zP9TCxmHYC9KYcKC

Merkle Root

246e6b8f7ae44fbc8a80e2b97d868fc42134d32521ee36c8fb05ad8e1d55d602

Transactions (2)

Coinbase658c96690eee4c…e57a3122f29ba7

1 in → 1 out8.5500 XPM111 B

AQVsUPfQ…YC9KYcKC

4b0c16afdbab8a…ffda96452bda78

5 in → 7 out18.7584 XPM923 B

AGrfqmnn…xgGemTu4 Ad5rowoZ…YCVsFMcc ARY4njt1…nHyFyfP6 ASdRf38U…Y2hPMApF ALAnEiVB…xvH3QqUj

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.

1.421 × 10⁹⁴(95-digit number)

14218723131446698025…64081415159561126399

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

1.421 × 10⁹⁴(95-digit number)

14218723131446698025…64081415159561126399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.421 × 10⁹⁴(95-digit number)

14218723131446698025…64081415159561126401

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

2.843 × 10⁹⁴(95-digit number)

28437446262893396050…28162830319122252799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.843 × 10⁹⁴(95-digit number)

28437446262893396050…28162830319122252801

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

5.687 × 10⁹⁴(95-digit number)

56874892525786792100…56325660638244505599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.687 × 10⁹⁴(95-digit number)

56874892525786792100…56325660638244505601

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

1.137 × 10⁹⁵(96-digit number)

11374978505157358420…12651321276489011199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.137 × 10⁹⁵(96-digit number)

11374978505157358420…12651321276489011201

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

2.274 × 10⁹⁵(96-digit number)

22749957010314716840…25302642552978022399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.274 × 10⁹⁵(96-digit number)

22749957010314716840…25302642552978022401

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 #505,548

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