Block #265,675

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/19/2013, 6:59:04 PM · Difficulty 9.9621 · 6,527,022 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f9e15d07664b7ec49d54d12e8086c334ccb8e372ed0060611bed79f36c68557c

View on Chainz ↗

Height

#265,675

Difficulty

9.962063

Transactions

Size

2.01 KB

Version

Bits

09f649c7

Nonce

41,628

Timestamp

11/19/2013, 6:59:04 PM

Confirmations

6,527,022

Merkle Root

d548e25234650f525e820abf5895427d2c09f86088e6983337f1571c2fc5e76b

Transactions (1)

Coinbased548e25234650f…f1571c2fc5e76b

1 in → 56 out10.0400 XPM1.92 KB

AW74jRHb…rgHeWWiu APZy8y6E…QZaGQjfp ALbnyRDo…sK52qx5d ANHbaxZp…XjnHCJJs AVzhvfTX…ZzNJYq61

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.

3.495 × 10⁹⁷(98-digit number)

34952176131088137250…72154922051760604639

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

3.495 × 10⁹⁷(98-digit number)

34952176131088137250…72154922051760604639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.495 × 10⁹⁷(98-digit number)

34952176131088137250…72154922051760604641

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

6.990 × 10⁹⁷(98-digit number)

69904352262176274500…44309844103521209279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.990 × 10⁹⁷(98-digit number)

69904352262176274500…44309844103521209281

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

1.398 × 10⁹⁸(99-digit number)

13980870452435254900…88619688207042418559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.398 × 10⁹⁸(99-digit number)

13980870452435254900…88619688207042418561

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

2.796 × 10⁹⁸(99-digit number)

27961740904870509800…77239376414084837119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.796 × 10⁹⁸(99-digit number)

27961740904870509800…77239376414084837121

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

5.592 × 10⁹⁸(99-digit number)

55923481809741019600…54478752828169674239

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