Block #494,444

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 4:28:16 AM · Difficulty 10.7184 · 6,322,660 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1aa7d75d065e952c718883c164bd003e3a1c09e0e5872ce91bad4949298a844d

View on Chainz ↗

Height

#494,444

Difficulty

10.718390

Transactions

Size

1.23 KB

Version

Bits

0ab7e86d

Nonce

215,813,755

Timestamp

4/16/2014, 4:28:16 AM

Confirmations

6,322,660

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

f215a781a923471af9b7d9dcccaf91c9bd5e58c1327752de143cf07d4adc46ed

Transactions (5)

Coinbasedf13a40b1e666d…ab2dd1a84da07f

1 in → 1 out8.7300 XPM116 B

AbwWkWZt…kawDhufa

d4f6a07bd55338…93b0027886ef79

1 in → 2 out4.5387 XPM225 B

AdMp3kEc…hv6Yr98E AYjwrrNa…p6r7yfsV

41e77b671ffe38…71aca04b6b1465

1 in → 2 out4.2738 XPM226 B

AM9hYVTV…StoKKo3r AHK1Apea…URE5hnSJ

9b674d865646bb…8a4cc07002f1a1

1 in → 2 out1.9143 XPM226 B

AKZ5RZTL…EU8xnSi5 AYrhRrv5…bYGwLj3U

6fadf1f9da62cc…687c57597d3a4d

2 in → 2 out1.4983 XPM375 B

AG8u7ddV…cU5QJSqk AJrwf3Kj…sECohDkc

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.

4.490 × 10⁹⁷(98-digit number)

44909994509842935091…37971647221659560799

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

4.490 × 10⁹⁷(98-digit number)

44909994509842935091…37971647221659560799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.490 × 10⁹⁷(98-digit number)

44909994509842935091…37971647221659560801

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

8.981 × 10⁹⁷(98-digit number)

89819989019685870182…75943294443319121599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.981 × 10⁹⁷(98-digit number)

89819989019685870182…75943294443319121601

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

1.796 × 10⁹⁸(99-digit number)

17963997803937174036…51886588886638243199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.796 × 10⁹⁸(99-digit number)

17963997803937174036…51886588886638243201

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

3.592 × 10⁹⁸(99-digit number)

35927995607874348073…03773177773276486399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.592 × 10⁹⁸(99-digit number)

35927995607874348073…03773177773276486401

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

7.185 × 10⁹⁸(99-digit number)

71855991215748696146…07546355546552972799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.185 × 10⁹⁸(99-digit number)

71855991215748696146…07546355546552972801

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 #494,444

Cookie Preferences