Block #265,624

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/19/2013, 5:55:15 PM · Difficulty 9.9621 · 6,525,319 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7306fad02ec2a0a78b85b94a4a040b7b8ab5f79170b09190c951829bffebb5fa

View on Chainz ↗

Height

#265,624

Difficulty

9.962122

Transactions

Size

867 B

Version

Bits

09f64da0

Nonce

52,567

Timestamp

11/19/2013, 5:55:15 PM

Confirmations

6,525,319

Merkle Root

bca967b1b2763fd3bd1879dbe9fc6498955a7e2ce5e27e83234b2ffaf59d69a9

Transactions (2)

Coinbasec650494f2c000c…755880238c981a

1 in → 1 out10.0700 XPM110 B

AeKNrjNj…1NEq95Ta

fc64d082d1a255…6211b997f43fc7

4 in → 2 out109.7868 XPM668 B

AcaqVy6b…8rPha8YP AJu6UaHB…bVNdCJAm

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.

1.873 × 10⁹³(94-digit number)

18737452014514395570…56431324162839021949

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

1.873 × 10⁹³(94-digit number)

18737452014514395570…56431324162839021949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.873 × 10⁹³(94-digit number)

18737452014514395570…56431324162839021951

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

3.747 × 10⁹³(94-digit number)

37474904029028791141…12862648325678043899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.747 × 10⁹³(94-digit number)

37474904029028791141…12862648325678043901

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

7.494 × 10⁹³(94-digit number)

74949808058057582282…25725296651356087799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.494 × 10⁹³(94-digit number)

74949808058057582282…25725296651356087801

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

1.498 × 10⁹⁴(95-digit number)

14989961611611516456…51450593302712175599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.498 × 10⁹⁴(95-digit number)

14989961611611516456…51450593302712175601

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

2.997 × 10⁹⁴(95-digit number)

29979923223223032912…02901186605424351199

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