Block #473,865

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 5:20:15 AM · Difficulty 10.4455 · 6,332,491 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ccb4d080cb4e681ba1e0e2df222f240127f585e9cfd8457917308fc77dd8d42d

View on Chainz ↗

Height

#473,865

Difficulty

10.445479

Transactions

Size

970 B

Version

Bits

0a720ae9

Nonce

103,452

Timestamp

4/4/2014, 5:20:15 AM

Confirmations

6,332,491

Mined by

⛏️ ;aS>@AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3582daa194f15f0923acac474cdb9b39299e1164e94abe46bbef4b1d02c7fa5d

Transactions (1)

Coinbase3582daa194f15f…ef4b1d02c7fa5d

1 in → 24 out9.1500 XPM879 B

AQvZBsUo…hppgRZTJ AJhUq5LB…kgcEVbqS AcaLouCs…xPDq8Sis AcVAEuoP…1jK61Unr ANNg88pG…ppn21sTe

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.

3.515 × 10⁹⁷(98-digit number)

35155693412156195354…20789655181004333719

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

3.515 × 10⁹⁷(98-digit number)

35155693412156195354…20789655181004333719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.515 × 10⁹⁷(98-digit number)

35155693412156195354…20789655181004333721

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

7.031 × 10⁹⁷(98-digit number)

70311386824312390709…41579310362008667439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.031 × 10⁹⁷(98-digit number)

70311386824312390709…41579310362008667441

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

1.406 × 10⁹⁸(99-digit number)

14062277364862478141…83158620724017334879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.406 × 10⁹⁸(99-digit number)

14062277364862478141…83158620724017334881

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

2.812 × 10⁹⁸(99-digit number)

28124554729724956283…66317241448034669759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.812 × 10⁹⁸(99-digit number)

28124554729724956283…66317241448034669761

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

5.624 × 10⁹⁸(99-digit number)

56249109459449912567…32634482896069339519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.624 × 10⁹⁸(99-digit number)

56249109459449912567…32634482896069339521

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 #473,865

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