Block #518,816

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2014, 9:25:36 PM · Difficulty 10.8542 · 6,286,228 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5122b8d9e0bc19f5161e20433ee9f9c256c88c449b812d31202709ad1dac737a

View on Chainz ↗

Height

#518,816

Difficulty

10.854189

Transactions

Size

1.33 KB

Version

Bits

0adaac27

Nonce

100,850

Timestamp

4/30/2014, 9:25:36 PM

Confirmations

6,286,228

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

7bfe4e133dd73af89b2d8df1bcb6c46d7aed31563cba43ed7eaed78f670308a6

Transactions (4)

Coinbase69674c6b720562…1db3a9f4744ad2

1 in → 1 out8.5000 XPM110 B

AeKNrjNj…1NEq95Ta

57e3293d05c6ed…a60c9d8c295b7a

2 in → 2 out14.2556 XPM375 B

ARVyuNS1…VNLEJUWY AQmgJPah…mv39DD7X

14aa90a0170281…5830600169bc9f

3 in → 4 out10.3424 XPM557 B

AeKNrjNj…1NEq95Ta AJ9HT2JV…tLekZoHB Ac5Sc2Mv…q4gm41o8 AcBvLaSu…X3gaHvJ1

136f3e20aed106…51c871a8e6883d

1 in → 2 out5.9255 XPM226 B

AGhk6PDb…sAw9Pe2B ATxoEAVm…o1hPnNf4

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.

3.554 × 10¹⁰⁰(101-digit number)

35548996711680469488…56379729604345364479

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

3.554 × 10¹⁰⁰(101-digit number)

35548996711680469488…56379729604345364479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.554 × 10¹⁰⁰(101-digit number)

35548996711680469488…56379729604345364481

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

7.109 × 10¹⁰⁰(101-digit number)

71097993423360938976…12759459208690728959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.109 × 10¹⁰⁰(101-digit number)

71097993423360938976…12759459208690728961

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

1.421 × 10¹⁰¹(102-digit number)

14219598684672187795…25518918417381457919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.421 × 10¹⁰¹(102-digit number)

14219598684672187795…25518918417381457921

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

2.843 × 10¹⁰¹(102-digit number)

28439197369344375590…51037836834762915839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.843 × 10¹⁰¹(102-digit number)

28439197369344375590…51037836834762915841

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

5.687 × 10¹⁰¹(102-digit number)

56878394738688751181…02075673669525831679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.687 × 10¹⁰¹(102-digit number)

56878394738688751181…02075673669525831681

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