Block #407,840

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2014, 6:13:11 AM · Difficulty 10.4290 · 6,397,183 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

964ca403559bdf9cf74fa17501322ef1447f19fbf647f01d48d3f46fa6c57372

View on Chainz ↗

Height

#407,840

Difficulty

10.429027

Transactions

Size

1.29 KB

Version

Bits

0a6dd4b5

Nonce

41,071

Timestamp

2/17/2014, 6:13:11 AM

Confirmations

6,397,183

Mined by

⛏️ P2SHAURSGouBo6GrLHSNHMuff5aXvtoF5scVKJ

Merkle Root

ddbb08cbf41be06fa2085953f9d2968857b5fe6243774cff0c1df5a02f3434bb

Transactions (4)

Coinbasef42e077f16eb24…441f0b94f058e9

1 in → 1 out9.2100 XPM111 B

AURSGouB…oF5scVKJ

a96b78d13709df…02aa7cee27b268

2 in → 2 out124.7100 XPM375 B

Adb2e49i…ETzM46fe AYMvUShC…UHmvswy7

81a4fc5d05d254…15079a425789b2

1 in → 2 out154.9400 XPM226 B

ANd6QFji…aH9wpttG Addcs943…97RFdqoL

e89f238c8538c4…608a1dadd93b6a

3 in → 2 out6.0339 XPM521 B

ANNExGuK…w9yJkSjL AUr4ic5U…WZTfhKcH

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.

1.918 × 10⁹⁹(100-digit number)

19185578218902415045…74829125113012266879

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

1.918 × 10⁹⁹(100-digit number)

19185578218902415045…74829125113012266879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.918 × 10⁹⁹(100-digit number)

19185578218902415045…74829125113012266881

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

3.837 × 10⁹⁹(100-digit number)

38371156437804830090…49658250226024533759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.837 × 10⁹⁹(100-digit number)

38371156437804830090…49658250226024533761

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

7.674 × 10⁹⁹(100-digit number)

76742312875609660181…99316500452049067519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.674 × 10⁹⁹(100-digit number)

76742312875609660181…99316500452049067521

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

1.534 × 10¹⁰⁰(101-digit number)

15348462575121932036…98633000904098135039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.534 × 10¹⁰⁰(101-digit number)

15348462575121932036…98633000904098135041

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

3.069 × 10¹⁰⁰(101-digit number)

30696925150243864072…97266001808196270079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.069 × 10¹⁰⁰(101-digit number)

30696925150243864072…97266001808196270081

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