Block #457,259

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 6:36:31 PM · Difficulty 10.4217 · 6,350,099 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c43559fd9c7bbdf390897c5610f63fd1bf2199633e8de6d5ce02728c0313e875

View on Chainz ↗

Height

#457,259

Difficulty

10.421732

Transactions

Size

2.43 KB

Version

Bits

0a6bf6a9

Nonce

165,248

Timestamp

3/23/2014, 6:36:31 PM

Confirmations

6,350,099

Mined by

⛏️ P2SHAbVqs978G4sxAgAicpHqEHvVbpqjT8Yhwb

Merkle Root

7172746d587453a7e83690071c7411320264e6a8d29aa9d4dc8e17ef660f7167

Transactions (5)

Coinbase28e7e1e89ee0cf…cb48083d59b87e

1 in → 1 out9.2500 XPM109 B

AbVqs978…qjT8Yhwb

203ef52a50703a…c1075560129551

8 in → 2 out14.0443 XPM1.23 KB

AQM1HjHw…34GAqCUP AV8bVVex…7EB4CTY8

5328881d31b7bd…f53918297684c3

1 in → 4 out35.9659 XPM293 B

AZ1BTjCh…JnBxH9Dq AVMEDKFe…DuPFrdw9 AegEGk5u…c5AnQ1n3 AHoENRJk…NhmYqijD

6d60eebd4d5865…01372c01f8341e

1 in → 4 out35.9655 XPM294 B

AegEGk5u…c5AnQ1n3 AZ1BTjCh…JnBxH9Dq AHoENRJk…NhmYqijD AMRu2Eym…BYWCmNp6

dc6914c3c3a97b…86f894cb8fa90b

2 in → 4 out13.7384 XPM443 B

AegEGk5u…c5AnQ1n3 AHoENRJk…NhmYqijD AZ1BTjCh…JnBxH9Dq AHDbTJHd…ZRMoDNQm

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.

4.248 × 10¹⁰¹(102-digit number)

42483791968347860902…99253536353525279999

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

4.248 × 10¹⁰¹(102-digit number)

42483791968347860902…99253536353525279999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.248 × 10¹⁰¹(102-digit number)

42483791968347860902…99253536353525280001

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

8.496 × 10¹⁰¹(102-digit number)

84967583936695721805…98507072707050559999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.496 × 10¹⁰¹(102-digit number)

84967583936695721805…98507072707050560001

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

1.699 × 10¹⁰²(103-digit number)

16993516787339144361…97014145414101119999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.699 × 10¹⁰²(103-digit number)

16993516787339144361…97014145414101120001

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

3.398 × 10¹⁰²(103-digit number)

33987033574678288722…94028290828202239999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.398 × 10¹⁰²(103-digit number)

33987033574678288722…94028290828202240001

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

6.797 × 10¹⁰²(103-digit number)

67974067149356577444…88056581656404479999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.797 × 10¹⁰²(103-digit number)

67974067149356577444…88056581656404480001

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 #457,259

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