Block #269,524

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 5:53:04 AM · Difficulty 9.9527 · 6,527,052 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

82b5b72ec522fd99ba266d761dcfe0d333c32262eed9b428a41178acddb8212b

View on Chainz ↗

Height

#269,524

Difficulty

9.952718

Transactions

Size

984 B

Version

Bits

09f3e551

Nonce

21,603

Timestamp

11/23/2013, 5:53:04 AM

Confirmations

6,527,052

Mined by

⛏️ P2SHAW1bodDG726kn45RB9FfbmpwhRcT3hsxUR

Merkle Root

ecdc91a86808de89857a842eb5e81f97d665291ecfd4e31edacfe27515c0557d

Transactions (2)

Coinbase02fdb39c14e041…499a20a72b0a8d

1 in → 1 out10.0900 XPM109 B

AW1bodDG…cT3hsxUR

06c2c79d4fcfae…786a7ca327e33b

5 in → 1 out0.5656 XPM785 B

ATNdaskg…bbGxYhxL

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.

3.176 × 10⁹⁵(96-digit number)

31760683154482343435…02084047330939161599

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

3.176 × 10⁹⁵(96-digit number)

31760683154482343435…02084047330939161599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.176 × 10⁹⁵(96-digit number)

31760683154482343435…02084047330939161601

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

6.352 × 10⁹⁵(96-digit number)

63521366308964686870…04168094661878323199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.352 × 10⁹⁵(96-digit number)

63521366308964686870…04168094661878323201

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

1.270 × 10⁹⁶(97-digit number)

12704273261792937374…08336189323756646399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.270 × 10⁹⁶(97-digit number)

12704273261792937374…08336189323756646401

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

2.540 × 10⁹⁶(97-digit number)

25408546523585874748…16672378647513292799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.540 × 10⁹⁶(97-digit number)

25408546523585874748…16672378647513292801

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

5.081 × 10⁹⁶(97-digit number)

50817093047171749496…33344757295026585599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.081 × 10⁹⁶(97-digit number)

50817093047171749496…33344757295026585601

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