Block #464,730

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2014, 11:45:33 PM · Difficulty 10.4221 · 6,345,898 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ac593e3cb40010cc49f22e48e6786a581ce2d91de09f43c3cd6457c32e5e7440

View on Chainz ↗

Height

#464,730

Difficulty

10.422070

Transactions

Size

1.07 KB

Version

Bits

0a6c0cc5

Nonce

4,095

Timestamp

3/28/2014, 11:45:33 PM

Confirmations

6,345,898

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

71d4562429b1f15ee879884908d428c1c45517db14a62718b63657ecd398fc35

Transactions (2)

Coinbaseab276c895183fc…9c0b4c783865bb

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

532e3faf8da583…1e712e7a6fa43e

5 in → 5 out12.3865 XPM888 B

AXSSYByb…8vG2sYWV AWZd8cAm…V3EwYpk7 ANQKf2g4…29NaVj23 AeKNrjNj…1NEq95Ta Ab1YTAY5…9zZqa2sB

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.

6.336 × 10⁹⁸(99-digit number)

63367297233798758802…44491286036013181399

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

6.336 × 10⁹⁸(99-digit number)

63367297233798758802…44491286036013181399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.336 × 10⁹⁸(99-digit number)

63367297233798758802…44491286036013181401

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 × 10⁹⁹(100-digit number)

12673459446759751760…88982572072026362799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.267 × 10⁹⁹(100-digit number)

12673459446759751760…88982572072026362801

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 × 10⁹⁹(100-digit number)

25346918893519503521…77965144144052725599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.534 × 10⁹⁹(100-digit number)

25346918893519503521…77965144144052725601

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

5.069 × 10⁹⁹(100-digit number)

50693837787039007042…55930288288105451199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.069 × 10⁹⁹(100-digit number)

50693837787039007042…55930288288105451201

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 × 10¹⁰⁰(101-digit number)

10138767557407801408…11860576576210902399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.013 × 10¹⁰⁰(101-digit number)

10138767557407801408…11860576576210902401

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 #464,730

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