Block #489,594

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/13/2014, 9:18:38 AM · Difficulty 10.6674 · 6,320,076 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eebfb180dee4e6a398b6108d570f3ffa00c6d3a5c31d85a45fedcffa1120aefe

View on Chainz ↗

Height

#489,594

Difficulty

10.667412

Transactions

Size

1.30 KB

Version

Bits

0aaadb89

Nonce

108,708,421

Timestamp

4/13/2014, 9:18:38 AM

Confirmations

6,320,076

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5d48b342a644f6bc40f1d7b316fa11f9ae6a2b9d2092d2455ce1acac79777253

Transactions (4)

Coinbase3d81b9420879bb…599f8f9a29c4df

1 in → 1 out8.8000 XPM116 B

AbwWkWZt…kawDhufa

b1babbe9826898…4e58444d588f62

1 in → 2 out7.2804 XPM226 B

AaJ5yqe7…Xmeo3fYk ALPvthUD…MYaYMDqP

c723ba34798912…84ef59e8bfc594

1 in → 2 out7.2755 XPM227 B

ATWZA6yR…2S7RB9ab APaZxKNd…W68WRdzm

5e48d1bf27b04c…70422830e6468e

4 in → 2 out1.0147 XPM671 B

AG7Y7aU6…BZ222DQW AHj2mxev…24XBnyfN

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.

7.473 × 10⁹⁷(98-digit number)

74733900973658474855…94016990218786801999

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

7.473 × 10⁹⁷(98-digit number)

74733900973658474855…94016990218786801999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.473 × 10⁹⁷(98-digit number)

74733900973658474855…94016990218786802001

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

1.494 × 10⁹⁸(99-digit number)

14946780194731694971…88033980437573603999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.494 × 10⁹⁸(99-digit number)

14946780194731694971…88033980437573604001

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

2.989 × 10⁹⁸(99-digit number)

29893560389463389942…76067960875147207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.989 × 10⁹⁸(99-digit number)

29893560389463389942…76067960875147208001

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

5.978 × 10⁹⁸(99-digit number)

59787120778926779884…52135921750294415999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.978 × 10⁹⁸(99-digit number)

59787120778926779884…52135921750294416001

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

1.195 × 10⁹⁹(100-digit number)

11957424155785355976…04271843500588831999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.195 × 10⁹⁹(100-digit number)

11957424155785355976…04271843500588832001

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 #489,594

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