Block #399,954

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 5:58:16 PM · Difficulty 10.4323 · 6,395,724 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0487a0f25e8afb14a37f024032ae502d471b7d95a694f3ef221ed84af69afbf6

View on Chainz ↗

Height

#399,954

Difficulty

10.432306

Transactions

Size

1.03 KB

Version

Bits

0a6eab9a

Nonce

219,329

Timestamp

2/11/2014, 5:58:16 PM

Confirmations

6,395,724

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

6063e3cc578761e57f5863fc7384949bf6cfad304188219cfd3ec4b9c95068ab

Transactions (3)

Coinbasea2fcc10c5b8beb…57c4c35bd5be46

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

5f49f3934b6753…64268cab7487b1

3 in → 7 out21.0243 XPM622 B

AY9tgoA9…kkkXTaFe AXwECA7B…7uyqxkcd AeR5xAAu…QS19drpA AZH3aBJB…T7FVgZ83 ALrZxq5u…jReX3z9e

c0597647d226aa…3cd8d51f6ec8f4

1 in → 2 out3.0116 XPM227 B

AbUA1vud…7KT3ZmeU AbPr7AWj…iF3Fxh14

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.

7.160 × 10⁹⁸(99-digit number)

71606959923344825210…51293048486680723079

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

7.160 × 10⁹⁸(99-digit number)

71606959923344825210…51293048486680723079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.160 × 10⁹⁸(99-digit number)

71606959923344825210…51293048486680723081

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

1.432 × 10⁹⁹(100-digit number)

14321391984668965042…02586096973361446159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.432 × 10⁹⁹(100-digit number)

14321391984668965042…02586096973361446161

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

2.864 × 10⁹⁹(100-digit number)

28642783969337930084…05172193946722892319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.864 × 10⁹⁹(100-digit number)

28642783969337930084…05172193946722892321

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

5.728 × 10⁹⁹(100-digit number)

57285567938675860168…10344387893445784639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.728 × 10⁹⁹(100-digit number)

57285567938675860168…10344387893445784641

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

1.145 × 10¹⁰⁰(101-digit number)

11457113587735172033…20688775786891569279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.145 × 10¹⁰⁰(101-digit number)

11457113587735172033…20688775786891569281

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