Block #468,525

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2014, 1:47:49 PM · Difficulty 10.4319 · 6,339,087 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

54990482374cf46c31dace6672ab586dd0c3f62964c7c04b63445e9119b3fc3d

View on Chainz ↗

Height

#468,525

Difficulty

10.431866

Transactions

Size

12.92 KB

Version

Bits

0a6e8ecd

Nonce

70,080

Timestamp

3/31/2014, 1:47:49 PM

Confirmations

6,339,087

Mined by

⛏️ P2SHAeavUDf5REE6PVJ3VSg4YPrY9ADqDizGbP

Merkle Root

6c98c99a2dc2fa233b5be35f7c8bc108fb8c199479055676255b7c13b733fadb

Transactions (4)

Coinbase5e5ec4c7a7ba06…124390defc4ec9

1 in → 1 out9.3100 XPM111 B

AeavUDf5…DqDizGbP

4f6cfb346130e3…ffe50695d2dd59

14 in → 51 out109.5085 XPM3.73 KB

APCzoU4y…kwX1GZVG Aepo3mhd…AwoPnjG3 AUkdqaxr…4jcbMUQ7 AKfwEQcv…uF2f3oRH AR8WV4KS…SChNuf3B

33f33ffe73213c…b2825975f128e1

3 in → 10 out27.5300 XPM693 B

AeKNrjNj…1NEq95Ta AGNcNsZk…FtABZTwX AKpWfTgS…JDmAtbgJ Aevqk5D4…9EsVdRX7 ALy7Ra4p…8KLmryJG

de251614b21515…190119246c7066

57 in → 2 out230.0118 XPM8.32 KB

ANdNpJWf…MHkvBWBj APhZbt91…ERWP9zpq

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.

2.894 × 10⁹⁷(98-digit number)

28943742074550180365…84558888088755691519

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

2.894 × 10⁹⁷(98-digit number)

28943742074550180365…84558888088755691519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.894 × 10⁹⁷(98-digit number)

28943742074550180365…84558888088755691521

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

5.788 × 10⁹⁷(98-digit number)

57887484149100360731…69117776177511383039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.788 × 10⁹⁷(98-digit number)

57887484149100360731…69117776177511383041

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

1.157 × 10⁹⁸(99-digit number)

11577496829820072146…38235552355022766079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.157 × 10⁹⁸(99-digit number)

11577496829820072146…38235552355022766081

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

2.315 × 10⁹⁸(99-digit number)

23154993659640144292…76471104710045532159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.315 × 10⁹⁸(99-digit number)

23154993659640144292…76471104710045532161

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

4.630 × 10⁹⁸(99-digit number)

46309987319280288585…52942209420091064319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.630 × 10⁹⁸(99-digit number)

46309987319280288585…52942209420091064321

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 #468,525

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