Block #468,341

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2014, 10:52:36 AM · Difficulty 10.4309 · 6,340,966 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c87645df8b9cae6978e3bd25c049b67ef6b4c721bee523d6f24270e540e5fceb

View on Chainz ↗

Height

#468,341

Difficulty

10.430851

Transactions

Size

1.07 KB

Version

Bits

0a6e4c3d

Nonce

127,285

Timestamp

3/31/2014, 10:52:36 AM

Confirmations

6,340,966

Mined by

⛏️ u%iAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

7a29412e645b8cf0ac33ad32019cc7a525a1eac2f70107d7e073a6f99cd1845c

Transactions (2)

Coinbase501f7080909b30…e17a73fca31394

1 in → 21 out9.1900 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH ATp4jJhs…TbSgR8Qb AUFKXvnz…342ApNcm

04a7fbbede42c5…42935d9f21d915

1 in → 2 out8.1443 XPM225 B

AUyx6Zc2…aZPWCMTP AUgdkRHJ…JFViE7Qv

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.

2.734 × 10⁹⁹(100-digit number)

27340303863578582816…57405125692918614079

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

2.734 × 10⁹⁹(100-digit number)

27340303863578582816…57405125692918614079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.734 × 10⁹⁹(100-digit number)

27340303863578582816…57405125692918614081

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

5.468 × 10⁹⁹(100-digit number)

54680607727157165632…14810251385837228159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.468 × 10⁹⁹(100-digit number)

54680607727157165632…14810251385837228161

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

1.093 × 10¹⁰⁰(101-digit number)

10936121545431433126…29620502771674456319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.093 × 10¹⁰⁰(101-digit number)

10936121545431433126…29620502771674456321

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

2.187 × 10¹⁰⁰(101-digit number)

21872243090862866252…59241005543348912639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.187 × 10¹⁰⁰(101-digit number)

21872243090862866252…59241005543348912641

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

4.374 × 10¹⁰⁰(101-digit number)

43744486181725732505…18482011086697825279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.374 × 10¹⁰⁰(101-digit number)

43744486181725732505…18482011086697825281

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 #468,341

Cookie Preferences