Block #470,518

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/1/2014, 11:01:14 PM · Difficulty 10.4335 · 6,345,947 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

759f93bf7e78d1e40abe4c40b9e34fb08bb3a5afbcd5154a3a794c88147d0215

View on Chainz ↗

Height

#470,518

Difficulty

10.433488

Transactions

Size

1.41 KB

Version

Bits

0a6ef90f

Nonce

20,181

Timestamp

4/1/2014, 11:01:14 PM

Confirmations

6,345,947

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

813d13007d1ac8f3604b7bd7df5e532aefeefcedde15a3169edf424301aecb0e

Transactions (4)

Coinbasedfba1df8192936…18603bc2dada02

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

57f249fb4bf994…22c4bece8daf1a

4 in → 2 out10.0100 XPM669 B

AHpBTQe4…uc2pi4KF AV4JxUvD…MKontNGN

235641aeac8c90…c874e82cf28b3c

1 in → 1 out9.2100 XPM191 B

AX68fSXw…sD9P3rs3

ebcc3e1a855a58…de6554942c768b

2 in → 2 out1.0104 XPM375 B

AHpBTQe4…uc2pi4KF Aey8mKBw…bymG7QUo

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.

3.179 × 10¹⁰⁰(101-digit number)

31792165492134805747…82593009805781507719

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

3.179 × 10¹⁰⁰(101-digit number)

31792165492134805747…82593009805781507719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.179 × 10¹⁰⁰(101-digit number)

31792165492134805747…82593009805781507721

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

6.358 × 10¹⁰⁰(101-digit number)

63584330984269611494…65186019611563015439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.358 × 10¹⁰⁰(101-digit number)

63584330984269611494…65186019611563015441

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

1.271 × 10¹⁰¹(102-digit number)

12716866196853922298…30372039223126030879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.271 × 10¹⁰¹(102-digit number)

12716866196853922298…30372039223126030881

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

2.543 × 10¹⁰¹(102-digit number)

25433732393707844597…60744078446252061759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.543 × 10¹⁰¹(102-digit number)

25433732393707844597…60744078446252061761

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

5.086 × 10¹⁰¹(102-digit number)

50867464787415689195…21488156892504123519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.086 × 10¹⁰¹(102-digit number)

50867464787415689195…21488156892504123521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.017 × 10¹⁰²(103-digit number)

10173492957483137839…42976313785008247039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #470,518

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