Block #464,065

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2014, 1:30:24 PM · Difficulty 10.4166 · 6,350,235 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

994e4c9efbad9bd04bce287ba56543f221fcfbd2eb4e4032a6cd24ca91b522c3

View on Chainz ↗

Height

#464,065

Difficulty

10.416596

Transactions

Size

1.02 KB

Version

Bits

0a6aa609

Nonce

414,069

Timestamp

3/28/2014, 1:30:24 PM

Confirmations

6,350,235

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

01a135d71e8cf2543a6444e44d98361d16cf7a8b5d9f5ff861c4817aa443cc07

Transactions (2)

Coinbase2679a519688b0f…4819d730b76bf9

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

4dcff34c760938…d955e3a427bbff

4 in → 10 out31.0016 XPM842 B

AUAVprvR…Q7nUDqV9 AJvKq8HD…WqkH2BmK AL9UZuKj…g3Q3eciV APn2wJAF…3buAhEQY AMyFarm4…6npGvxsv

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.

4.733 × 10¹⁰⁰(101-digit number)

47336511306717735072…16317037904745676799

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

4.733 × 10¹⁰⁰(101-digit number)

47336511306717735072…16317037904745676799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.733 × 10¹⁰⁰(101-digit number)

47336511306717735072…16317037904745676801

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

9.467 × 10¹⁰⁰(101-digit number)

94673022613435470145…32634075809491353599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.467 × 10¹⁰⁰(101-digit number)

94673022613435470145…32634075809491353601

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

1.893 × 10¹⁰¹(102-digit number)

18934604522687094029…65268151618982707199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.893 × 10¹⁰¹(102-digit number)

18934604522687094029…65268151618982707201

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

3.786 × 10¹⁰¹(102-digit number)

37869209045374188058…30536303237965414399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.786 × 10¹⁰¹(102-digit number)

37869209045374188058…30536303237965414401

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

7.573 × 10¹⁰¹(102-digit number)

75738418090748376116…61072606475930828799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.573 × 10¹⁰¹(102-digit number)

75738418090748376116…61072606475930828801

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 #464,065

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