Block #1,445,812

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/7/2016, 1:05:19 AM · Difficulty 10.7588 · 5,387,173 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a1fd4ce6b4c4581276d570a10f07f123d2bfef76d75f4f40c3fc92a09c9586e6

View on Chainz ↗

Height

#1,445,812

Difficulty

10.758823

Transactions

Size

833 B

Version

Bits

0ac2423e

Nonce

426,060,578

Timestamp

2/7/2016, 1:05:19 AM

Confirmations

5,387,173

Mined by

⛏️ P2SHAT17jbx817HFpete96j5qMYk6Eb5qSUnc2

Merkle Root

af7b51d88dfb3278a33b0c077f7a936dfd81a09338149f953a8071a8aa05ee64

Transactions (2)

Coinbasec44f92a84deb6e…77a5acffbfa00c

1 in → 1 out8.6400 XPM109 B

AT17jbx8…b5qSUnc2

631f06563ecc08…7a5f3e4661c348

1 in → 14 out14.9156 XPM634 B

AXQWybBH…EsqASaBv AQNxWM4L…s8yndBor ASXaymMq…xQTJu4rm AXJWzk53…dCACQMVX Absz1uE2…uktJpz9F

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.

4.953 × 10⁹⁵(96-digit number)

49538593381663066960…94828492079174204479

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

4.953 × 10⁹⁵(96-digit number)

49538593381663066960…94828492079174204479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.953 × 10⁹⁵(96-digit number)

49538593381663066960…94828492079174204481

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

9.907 × 10⁹⁵(96-digit number)

99077186763326133920…89656984158348408959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.907 × 10⁹⁵(96-digit number)

99077186763326133920…89656984158348408961

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

1.981 × 10⁹⁶(97-digit number)

19815437352665226784…79313968316696817919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.981 × 10⁹⁶(97-digit number)

19815437352665226784…79313968316696817921

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

3.963 × 10⁹⁶(97-digit number)

39630874705330453568…58627936633393635839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.963 × 10⁹⁶(97-digit number)

39630874705330453568…58627936633393635841

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

7.926 × 10⁹⁶(97-digit number)

79261749410660907136…17255873266787271679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.926 × 10⁹⁶(97-digit number)

79261749410660907136…17255873266787271681

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 #1,445,812

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