Block #353,481

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2014, 11:23:47 PM · Difficulty 10.3270 · 6,450,050 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3e5e7a6c07c0420da6b2e0d20c4e549ccb7cd244f912e36e87e95b11d3c549f4

View on Chainz ↗

Height

#353,481

Difficulty

10.326954

Transactions

Size

1.05 KB

Version

Bits

0a53b33f

Nonce

3,060

Timestamp

1/10/2014, 11:23:47 PM

Confirmations

6,450,050

Mined by

⛏️ daRpAQ8QAT3JKsV1xD6zC94z9djnpJrCFKuVbR

Merkle Root

e723be971976f964ae6e3dfe812c4dfbab51b4d6b8aee3d2af3abe7569199e72

Transactions (1)

Coinbasee723be971976f9…3abe7569199e72

1 in → 27 out9.3600 XPM981 B

AQ8QAT3J…rCFKuVbR Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AdwTEXyC…NwbVbqZV AL8CJrXc…ReWqhicJ

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.

4.313 × 10⁹⁸(99-digit number)

43137658304928042034…32534508969632259999

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

4.313 × 10⁹⁸(99-digit number)

43137658304928042034…32534508969632259999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.313 × 10⁹⁸(99-digit number)

43137658304928042034…32534508969632260001

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

8.627 × 10⁹⁸(99-digit number)

86275316609856084069…65069017939264519999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.627 × 10⁹⁸(99-digit number)

86275316609856084069…65069017939264520001

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

1.725 × 10⁹⁹(100-digit number)

17255063321971216813…30138035878529039999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.725 × 10⁹⁹(100-digit number)

17255063321971216813…30138035878529040001

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

3.451 × 10⁹⁹(100-digit number)

34510126643942433627…60276071757058079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.451 × 10⁹⁹(100-digit number)

34510126643942433627…60276071757058080001

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

6.902 × 10⁹⁹(100-digit number)

69020253287884867255…20552143514116159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.902 × 10⁹⁹(100-digit number)

69020253287884867255…20552143514116160001

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