Block #645,149

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/23/2014, 8:05:48 PM · Difficulty 10.9541 · 6,146,791 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b4a9676402d62115df645e4bddd2e633d8107c067e0b5da6c78c8e946f1d5f22

View on Chainz ↗

Height

#645,149

Difficulty

10.954072

Transactions

Size

1.33 KB

Version

Bits

0af43e0c

Nonce

1,793,765,361

Timestamp

7/23/2014, 8:05:48 PM

Confirmations

6,146,791

Merkle Root

ccd1c906b1a5cd37c3e4dfa204375c1db479bc7e2a1c193b0a4bbb1d1070d415

Transactions (4)

Coinbase94a409cf3231df…bc0afd9a6836d0

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

88998d80098462…efa4e74ee60523

3 in → 2 out20.8613 XPM523 B

AaU9J1Lk…4e47uLfq AcWvp5L3…NUBu1w8D

a9433759c14332…a9fd314495da5c

2 in → 3 out4.5382 XPM409 B

AeKNrjNj…1NEq95Ta AWQhak32…eArVqMxc ANCZAhFA…4XJ8NSvi

3534d6705267d6…441223aee52c56

1 in → 2 out1.0488 XPM225 B

Ae7ht6Sj…7i8cq412 AXJnVaxu…BNdb8wFm

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.

4.779 × 10¹⁰⁰(101-digit number)

47792561297002201992…31992066317310443519

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

4.779 × 10¹⁰⁰(101-digit number)

47792561297002201992…31992066317310443519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.779 × 10¹⁰⁰(101-digit number)

47792561297002201992…31992066317310443521

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

9.558 × 10¹⁰⁰(101-digit number)

95585122594004403985…63984132634620887039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.558 × 10¹⁰⁰(101-digit number)

95585122594004403985…63984132634620887041

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

1.911 × 10¹⁰¹(102-digit number)

19117024518800880797…27968265269241774079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.911 × 10¹⁰¹(102-digit number)

19117024518800880797…27968265269241774081

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

3.823 × 10¹⁰¹(102-digit number)

38234049037601761594…55936530538483548159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.823 × 10¹⁰¹(102-digit number)

38234049037601761594…55936530538483548161

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

7.646 × 10¹⁰¹(102-digit number)

76468098075203523188…11873061076967096319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.646 × 10¹⁰¹(102-digit number)

76468098075203523188…11873061076967096321

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