Block #475,362

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 4:44:52 AM · Difficulty 10.4562 · 6,317,411 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7b4bd6bbe291df55a227176eabb71486d56f9eb1e8e260a54f540faf79a22edb

View on Chainz ↗

Height

#475,362

Difficulty

10.456207

Transactions

Size

936 B

Version

Bits

0a74c9f6

Nonce

25,474

Timestamp

4/5/2014, 4:44:52 AM

Confirmations

6,317,411

Merkle Root

8f91105d3a402645e0ffd339a496e2915bfae19288e042a805dc06805196d8a9

Transactions (1)

Coinbase8f91105d3a4026…dc06805196d8a9

1 in → 23 out9.1300 XPM845 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn

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.

4.007 × 10⁹⁷(98-digit number)

40079776142431386154…88654521081120163839

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

4.007 × 10⁹⁷(98-digit number)

40079776142431386154…88654521081120163839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.007 × 10⁹⁷(98-digit number)

40079776142431386154…88654521081120163841

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

8.015 × 10⁹⁷(98-digit number)

80159552284862772309…77309042162240327679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.015 × 10⁹⁷(98-digit number)

80159552284862772309…77309042162240327681

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

1.603 × 10⁹⁸(99-digit number)

16031910456972554461…54618084324480655359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.603 × 10⁹⁸(99-digit number)

16031910456972554461…54618084324480655361

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

3.206 × 10⁹⁸(99-digit number)

32063820913945108923…09236168648961310719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.206 × 10⁹⁸(99-digit number)

32063820913945108923…09236168648961310721

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

6.412 × 10⁹⁸(99-digit number)

64127641827890217847…18472337297922621439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.412 × 10⁹⁸(99-digit number)

64127641827890217847…18472337297922621441

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