Block #442,717

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 12:57:13 AM · Difficulty 10.3492 · 6,353,346 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6817054eaf75b7c82f121eabf8ee1d3d87ed3fd8f6b705b2cd720548f31da5c7

View on Chainz ↗

Height

#442,717

Difficulty

10.349184

Transactions

Size

892 B

Version

Bits

0a596420

Nonce

75,330

Timestamp

3/14/2014, 12:57:13 AM

Confirmations

6,353,346

Mined by

⛏️ P2SHAZwvxxWZJnieGQ6vSRu3zh3vSdRJsTWMbj

Merkle Root

26131d0085ae5f748c32e48eb96b7f5dee8eeb3f5d0db76e1226b743887b5487

Transactions (2)

Coinbase7ff9efbd44a6c7…f025dcc7cb0fee

1 in → 1 out9.3300 XPM109 B

AZwvxxWZ…RJsTWMbj

4a9b74baa1656c…4311bd25fd4f2a

3 in → 10 out28.8400 XPM693 B

Acjw5rzo…872kPK2w AaPxPznh…FjUB1Swp AFmv5mWD…urvyngVQ AJvKq8HD…WqkH2BmK AP5i7QoC…HmBrELxR

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.

6.335 × 10⁹³(94-digit number)

63352927917834752276…41945150110253818239

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

6.335 × 10⁹³(94-digit number)

63352927917834752276…41945150110253818239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.335 × 10⁹³(94-digit number)

63352927917834752276…41945150110253818241

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

1.267 × 10⁹⁴(95-digit number)

12670585583566950455…83890300220507636479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.267 × 10⁹⁴(95-digit number)

12670585583566950455…83890300220507636481

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

2.534 × 10⁹⁴(95-digit number)

25341171167133900910…67780600441015272959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.534 × 10⁹⁴(95-digit number)

25341171167133900910…67780600441015272961

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

5.068 × 10⁹⁴(95-digit number)

50682342334267801821…35561200882030545919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.068 × 10⁹⁴(95-digit number)

50682342334267801821…35561200882030545921

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

1.013 × 10⁹⁵(96-digit number)

10136468466853560364…71122401764061091839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.013 × 10⁹⁵(96-digit number)

10136468466853560364…71122401764061091841

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