Block #2,468,089

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/11/2018, 1:32:21 PM · Difficulty 10.9603 · 4,371,262 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f6710f16e7ab9eb2f51bca32cdf9a211190a1a9071cb06eab5d9d99faf978021

View on Chainz ↗

Height

#2,468,089

Difficulty

10.960340

Transactions

Size

1.62 KB

Version

Bits

0af5d8d0

Nonce

2,047,593,614

Timestamp

1/11/2018, 1:32:21 PM

Confirmations

4,371,262

Mined by

⛏️ P2SHAP3jnAXqR2uNXkvzqbbPvDkHQ94AQkoS9L

Merkle Root

0749d201f7525797d3bd767fb39adfd2fceebc0e971c28e9fb6336ffc419a771

Transactions (5)

Coinbase2af288cb706167…2fa4b8310ec9e7

1 in → 1 out8.3500 XPM109 B

AP3jnAXq…4AQkoS9L

a3df1318b8cce7…dd23c8b405c2bd

1 in → 2 out11.4084 XPM225 B

APBM2w7U…Qx6F7p89 AW1EZbjk…BuohuevN

93a564754953ac…dbaf50fd2215f2

1 in → 2 out8.3000 XPM193 B

AaUjgbny…KoYqKQYU AYqxcMYZ…H6RQSKHK

f94dcc60c45080…0b2646dcdf1582

1 in → 2 out4.1241 XPM225 B

APxYMUyJ…TbDwyQN8 AeYZTP6b…v53Q54vJ

ada2f9824b2a3e…3812e04c7e9e4a

5 in → 2 out4.0293 XPM817 B

AdBsiaeP…pbaJN3VP ANxNfXmZ…4p5PaHCM

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.

5.095 × 10⁹⁴(95-digit number)

50957833982706418213…30700146240048929919

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

5.095 × 10⁹⁴(95-digit number)

50957833982706418213…30700146240048929919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.095 × 10⁹⁴(95-digit number)

50957833982706418213…30700146240048929921

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

1.019 × 10⁹⁵(96-digit number)

10191566796541283642…61400292480097859839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.019 × 10⁹⁵(96-digit number)

10191566796541283642…61400292480097859841

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

2.038 × 10⁹⁵(96-digit number)

20383133593082567285…22800584960195719679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.038 × 10⁹⁵(96-digit number)

20383133593082567285…22800584960195719681

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

4.076 × 10⁹⁵(96-digit number)

40766267186165134570…45601169920391439359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.076 × 10⁹⁵(96-digit number)

40766267186165134570…45601169920391439361

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

8.153 × 10⁹⁵(96-digit number)

81532534372330269140…91202339840782878719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.153 × 10⁹⁵(96-digit number)

81532534372330269140…91202339840782878721

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 #2,468,089

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