Block #65,454

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 12:21:38 PM · Difficulty 8.9842 · 6,733,894 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1f2e5995bfe5b4086fde9c35b9ed1ccea4cc6f1237656584938c9601247a211a

View on Chainz ↗

Height

#65,454

Difficulty

8.984177

Transactions

Size

2.59 KB

Version

Bits

08fbf30d

Nonce

280

Timestamp

7/19/2013, 12:21:38 PM

Confirmations

6,733,894

Mined by

⛏️ P2SHATkPCNiuYBqcNeSBc2y1E58R3MsUjt7RrN

Merkle Root

2a3a57034da228b5d9e19bd71a5755dbf25f18d36b062c49399625a47d13a24e

Transactions (3)

Coinbasece60490e577031…7a19553905c010

1 in → 1 out12.4100 XPM110 B

ATkPCNiu…sUjt7RrN

2067dc2b506a40…ff64d845b95ec7

13 in → 1 out700.0000 XPM1.89 KB

AQtw2B2f…FkAscNS7

def04be66b38af…4db6d931b12a31

3 in → 2 out178.0400 XPM521 B

AHt5hJrd…7KEG2WHr ANkHsWm5…QYcNQ2pF

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.

3.264 × 10⁹⁰(91-digit number)

32645354014971428225…67783612381650295159

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

3.264 × 10⁹⁰(91-digit number)

32645354014971428225…67783612381650295159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.264 × 10⁹⁰(91-digit number)

32645354014971428225…67783612381650295161

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

6.529 × 10⁹⁰(91-digit number)

65290708029942856451…35567224763300590319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.529 × 10⁹⁰(91-digit number)

65290708029942856451…35567224763300590321

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

1.305 × 10⁹¹(92-digit number)

13058141605988571290…71134449526601180639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.305 × 10⁹¹(92-digit number)

13058141605988571290…71134449526601180641

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

2.611 × 10⁹¹(92-digit number)

26116283211977142580…42268899053202361279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.611 × 10⁹¹(92-digit number)

26116283211977142580…42268899053202361281

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

5.223 × 10⁹¹(92-digit number)

52232566423954285161…84537798106404722559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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