Block #563,183

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/26/2014, 6:43:57 PM · Difficulty 10.9648 · 6,247,140 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c55f512c49fa541908faa71eafd8e3ea443ecda550d4833a6928dd9013353399

View on Chainz ↗

Height

#563,183

Difficulty

10.964803

Transactions

Size

808 B

Version

Bits

0af6fd4c

Nonce

2,335,829,619

Timestamp

5/26/2014, 6:43:57 PM

Confirmations

6,247,140

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e0a610bcf833dca590f88463ddb66a6054cb1f4dbca4405d20fab2a709ebb9bf

Transactions (3)

Coinbasebbfa2ca961e142…08d2bff126fca1

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

70be675de65efb…3d4a4839c21e12

1 in → 2 out4.7193 XPM225 B

AJ71Vsdu…kvNE8zX5 AQK97f8L…hruscYGC

c6ae54bac910e6…94d9c70ac2bb34

2 in → 2 out0.7137 XPM375 B

APHx196W…DwkgXfoX AJP7Wp1A…PrKdu922

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.

2.182 × 10¹⁰⁰(101-digit number)

21827222310762110287…44001625438505374719

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

2.182 × 10¹⁰⁰(101-digit number)

21827222310762110287…44001625438505374719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.182 × 10¹⁰⁰(101-digit number)

21827222310762110287…44001625438505374721

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

4.365 × 10¹⁰⁰(101-digit number)

43654444621524220575…88003250877010749439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.365 × 10¹⁰⁰(101-digit number)

43654444621524220575…88003250877010749441

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

8.730 × 10¹⁰⁰(101-digit number)

87308889243048441151…76006501754021498879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.730 × 10¹⁰⁰(101-digit number)

87308889243048441151…76006501754021498881

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

1.746 × 10¹⁰¹(102-digit number)

17461777848609688230…52013003508042997759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.746 × 10¹⁰¹(102-digit number)

17461777848609688230…52013003508042997761

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

3.492 × 10¹⁰¹(102-digit number)

34923555697219376460…04026007016085995519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.492 × 10¹⁰¹(102-digit number)

34923555697219376460…04026007016085995521

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 #563,183

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