Block #483,425

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2014, 1:27:11 AM · Difficulty 10.5566 · 6,333,388 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

58075e6ac72a5958a4950e94346dfefd5c9a345663fb3eb0a5744aeb91b03d67

View on Chainz ↗

Height

#483,425

Difficulty

10.556639

Transactions

Size

25.49 KB

Version

Bits

0a8e7fed

Nonce

433,969,767

Timestamp

4/10/2014, 1:27:11 AM

Confirmations

6,333,388

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

f06d25276343a689f1f278864be91d09ac28c62a680a451ae14b758820bf35bc

Transactions (3)

Coinbasef9e319b4982573…d1c81e2ecd5ed4

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

a896089be0e56d…0068e7bf68c7be

4 in → 9 out27.1560 XPM805 B

AeKNrjNj…1NEq95Ta ARu3a61w…jzkc9KSg AUhSALWL…rMjknJuF AU328Zva…1UF3tiZF AZwXBq4j…rzStTzBk

ad88c2b46ead38…b661d8b2e4eb13

169 in → 2 out100.0100 XPM24.50 KB

AJME8fpz…SV7y9UwA AbzFSGHz…oUxJgWE3

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.

2.510 × 10⁹⁷(98-digit number)

25106586269293183626…20039524902350867199

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

2.510 × 10⁹⁷(98-digit number)

25106586269293183626…20039524902350867199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.510 × 10⁹⁷(98-digit number)

25106586269293183626…20039524902350867201

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

5.021 × 10⁹⁷(98-digit number)

50213172538586367253…40079049804701734399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.021 × 10⁹⁷(98-digit number)

50213172538586367253…40079049804701734401

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

1.004 × 10⁹⁸(99-digit number)

10042634507717273450…80158099609403468799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.004 × 10⁹⁸(99-digit number)

10042634507717273450…80158099609403468801

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

2.008 × 10⁹⁸(99-digit number)

20085269015434546901…60316199218806937599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.008 × 10⁹⁸(99-digit number)

20085269015434546901…60316199218806937601

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

4.017 × 10⁹⁸(99-digit number)

40170538030869093802…20632398437613875199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.017 × 10⁹⁸(99-digit number)

40170538030869093802…20632398437613875201

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 #483,425

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