Block #473,881

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 5:40:44 AM · Difficulty 10.4449 · 6,335,622 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

00c016bda1eee3c348099fc27a0aaf50e93bd634f71366846ea1b6ac464236c2

View on Chainz ↗

Height

#473,881

Difficulty

10.444931

Transactions

Size

969 B

Version

Bits

0a71e704

Nonce

9,954

Timestamp

4/4/2014, 5:40:44 AM

Confirmations

6,335,622

Mined by

⛏️ ;aS>EAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

a22639cd41c0b3a55a6b3e93b54dd894c07b12e614fd7240fb3da4e798a82fc3

Transactions (1)

Coinbasea22639cd41c0b3…3da4e798a82fc3

1 in → 24 out9.1500 XPM879 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AdiJnPZ2…8NEy6P8S

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.

4.053 × 10⁹⁴(95-digit number)

40532916654440518261…35723411599695314879

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

4.053 × 10⁹⁴(95-digit number)

40532916654440518261…35723411599695314879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.053 × 10⁹⁴(95-digit number)

40532916654440518261…35723411599695314881

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

8.106 × 10⁹⁴(95-digit number)

81065833308881036523…71446823199390629759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.106 × 10⁹⁴(95-digit number)

81065833308881036523…71446823199390629761

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

1.621 × 10⁹⁵(96-digit number)

16213166661776207304…42893646398781259519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.621 × 10⁹⁵(96-digit number)

16213166661776207304…42893646398781259521

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

3.242 × 10⁹⁵(96-digit number)

32426333323552414609…85787292797562519039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.242 × 10⁹⁵(96-digit number)

32426333323552414609…85787292797562519041

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

6.485 × 10⁹⁵(96-digit number)

64852666647104829218…71574585595125038079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.485 × 10⁹⁵(96-digit number)

64852666647104829218…71574585595125038081

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 #473,881

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