Block #385,905

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2014, 3:02:20 AM · Difficulty 10.4047 · 6,421,278 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d24367f957f69d1743135f10e6cca21055ee4d2a503cd50acab983d6b1a2d06b

View on Chainz ↗

Height

#385,905

Difficulty

10.404686

Transactions

Size

3.50 KB

Version

Bits

0a679988

Nonce

480,336

Timestamp

2/2/2014, 3:02:20 AM

Confirmations

6,421,278

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

6b1fa060eb49b5ed2665f1121229fb96e52d84282b10de4f182927e8318a3a59

Transactions (5)

Coinbase7673631f1e4cbe…a9a5a62cb908a3

1 in → 1 out9.2900 XPM110 B

AeKNrjNj…1NEq95Ta

f2e634d8869888…cfc710246d2a7f

17 in → 1 out17.1211 XPM2.50 KB

Ac37ttP4…mGamF24R

eac1d1f4654f4a…74395417be83a6

2 in → 2 out4.9731 XPM375 B

APNaRuCP…LJwzA4a6 AcKeCj8g…9w2DbGVP

9f2ebed1b3b80d…ff288514e31954

1 in → 2 out1.2300 XPM225 B

APovVvrg…hveteWrz ATEHkpGw…ov1zpovZ

9c36874d877f13…a45ce0f3724ebc

1 in → 2 out8.1236 XPM226 B

ANA5H8Zb…i8tWmqVg ALau3Cn2…dA1yVZGm

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.

1.256 × 10¹⁰²(103-digit number)

12569863410943308228…97245525222486583999

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

1.256 × 10¹⁰²(103-digit number)

12569863410943308228…97245525222486583999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.256 × 10¹⁰²(103-digit number)

12569863410943308228…97245525222486584001

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

2.513 × 10¹⁰²(103-digit number)

25139726821886616456…94491050444973167999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.513 × 10¹⁰²(103-digit number)

25139726821886616456…94491050444973168001

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

5.027 × 10¹⁰²(103-digit number)

50279453643773232912…88982100889946335999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.027 × 10¹⁰²(103-digit number)

50279453643773232912…88982100889946336001

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

1.005 × 10¹⁰³(104-digit number)

10055890728754646582…77964201779892671999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.005 × 10¹⁰³(104-digit number)

10055890728754646582…77964201779892672001

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

2.011 × 10¹⁰³(104-digit number)

20111781457509293165…55928403559785343999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.011 × 10¹⁰³(104-digit number)

20111781457509293165…55928403559785344001

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 #385,905

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