Block #264,301

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/18/2013, 1:55:33 PM · Difficulty 9.9647 · 6,539,085 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

37859a1168746ff17a9e195f6fb4c54ac8500fffaec6289dc96f5319ddd962fb

View on Chainz ↗

Height

#264,301

Difficulty

9.964683

Transactions

Size

1.58 KB

Version

Bits

09f6f57d

Nonce

70,434

Timestamp

11/18/2013, 1:55:33 PM

Confirmations

6,539,085

Mined by

⛏️ P2SHAULHqwwdTADHKs4RRemhqfb5L21m9NcYZd

Merkle Root

978e7daab17261f00b333ea7c7bef40d7d8ea2b0fd5cd0896aa1e506f47dc391

Transactions (4)

Coinbaseef268ae8c38f7a…057149409e0f78

1 in → 1 out10.0900 XPM109 B

AULHqwwd…1m9NcYZd

79f56abd5400d5…a2313c9901007c

4 in → 2 out204.6081 XPM670 B

AZdmkNt9…Dk8ffFeU Ab6yYkyG…RFk272PK

b2bc113b907a5f…7b1c39da0b7343

3 in → 2 out3.3800 XPM520 B

ATJVKJ96…FLqKgyoi APpcxdEv…GGyzJj4r

bf4d5e997fac04…140c8ac177819a

1 in → 2 out2.9900 XPM226 B

AcbJmZ6i…bed9N1wk APTudnFY…3SrjMLfs

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.

4.133 × 10⁹⁵(96-digit number)

41339826965777975261…00304862539952871999

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

4.133 × 10⁹⁵(96-digit number)

41339826965777975261…00304862539952871999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.133 × 10⁹⁵(96-digit number)

41339826965777975261…00304862539952872001

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

8.267 × 10⁹⁵(96-digit number)

82679653931555950522…00609725079905743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.267 × 10⁹⁵(96-digit number)

82679653931555950522…00609725079905744001

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

1.653 × 10⁹⁶(97-digit number)

16535930786311190104…01219450159811487999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.653 × 10⁹⁶(97-digit number)

16535930786311190104…01219450159811488001

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

3.307 × 10⁹⁶(97-digit number)

33071861572622380209…02438900319622975999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.307 × 10⁹⁶(97-digit number)

33071861572622380209…02438900319622976001

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

6.614 × 10⁹⁶(97-digit number)

66143723145244760418…04877800639245951999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.614 × 10⁹⁶(97-digit number)

66143723145244760418…04877800639245952001

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