Block #424,962

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/1/2014, 1:34:47 PM · Difficulty 10.3657 · 6,370,890 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d039f7c9fa007f7953fe9de56972c690390df29e236178622a2d9be09baefc84

View on Chainz ↗

Height

#424,962

Difficulty

10.365749

Transactions

Size

433 B

Version

Bits

0a5da1b7

Nonce

46,028

Timestamp

3/1/2014, 1:34:47 PM

Confirmations

6,370,890

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e36a235c88f7752f3f05d25079f2af12e2cf04a2488b8351a913ca8dfb7c1c9a

Transactions (2)

Coinbaseb3baa54315acbb…2fc19bde18978a

1 in → 1 out9.3000 XPM116 B

AbwWkWZt…kawDhufa

d481e7cc6636b4…a8b0d513887559

1 in → 2 out3.0724 XPM226 B

AWSEfHgJ…cAriYmNe ASX54aVf…NtbYmxpx

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.

1.629 × 10⁹⁷(98-digit number)

16298830606781083677…56766431264453596859

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

1.629 × 10⁹⁷(98-digit number)

16298830606781083677…56766431264453596859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.629 × 10⁹⁷(98-digit number)

16298830606781083677…56766431264453596861

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

3.259 × 10⁹⁷(98-digit number)

32597661213562167355…13532862528907193719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.259 × 10⁹⁷(98-digit number)

32597661213562167355…13532862528907193721

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

6.519 × 10⁹⁷(98-digit number)

65195322427124334711…27065725057814387439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.519 × 10⁹⁷(98-digit number)

65195322427124334711…27065725057814387441

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

1.303 × 10⁹⁸(99-digit number)

13039064485424866942…54131450115628774879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.303 × 10⁹⁸(99-digit number)

13039064485424866942…54131450115628774881

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

2.607 × 10⁹⁸(99-digit number)

26078128970849733884…08262900231257549759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.607 × 10⁹⁸(99-digit number)

26078128970849733884…08262900231257549761

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