Block #863,253

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/22/2014, 9:04:01 AM · Difficulty 10.9628 · 5,940,353 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ba9acb23ee4887ce3bb4ee9f90b9519467e4cf8066612454880ac3e4cb77a657

View on Chainz ↗

Height

#863,253

Difficulty

10.962792

Transactions

Size

95.32 KB

Version

Bits

0af67988

Nonce

538,210,564

Timestamp

12/22/2014, 9:04:01 AM

Confirmations

5,940,353

Mined by

⛏️ P2SHAUXf9MrcHaCxN8hfgpmnrWpWxfuGF7GAsz

Merkle Root

0049430ec9fb42abd9aa2ad476c8b2826cf33424ba0538dbd0dd261104513729

Transactions (3)

Coinbase68b3e724c6ecb2…12661f3d42157f

1 in → 1 out9.3000 XPM110 B

AUXf9Mrc…uGF7GAsz

ce8e452a2a32a8…e2a1f14973ccfc

643 in → 2 out2117.7481 XPM93.03 KB

AXxcDPam…Bu4Ksq49 AGF9otCw…WcgRPjsA

2ba8733bd65b56…a84954058d1410

14 in → 2 out100.1200 XPM2.09 KB

ARckuVkB…wd96ugKD ANM8MXXm…oKFSAKqj

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.

1.561 × 10⁹⁵(96-digit number)

15612417732928931534…54070591871682135039

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

1.561 × 10⁹⁵(96-digit number)

15612417732928931534…54070591871682135039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.561 × 10⁹⁵(96-digit number)

15612417732928931534…54070591871682135041

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

3.122 × 10⁹⁵(96-digit number)

31224835465857863068…08141183743364270079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.122 × 10⁹⁵(96-digit number)

31224835465857863068…08141183743364270081

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

6.244 × 10⁹⁵(96-digit number)

62449670931715726137…16282367486728540159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.244 × 10⁹⁵(96-digit number)

62449670931715726137…16282367486728540161

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

1.248 × 10⁹⁶(97-digit number)

12489934186343145227…32564734973457080319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.248 × 10⁹⁶(97-digit number)

12489934186343145227…32564734973457080321

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

2.497 × 10⁹⁶(97-digit number)

24979868372686290454…65129469946914160639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.497 × 10⁹⁶(97-digit number)

24979868372686290454…65129469946914160641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.995 × 10⁹⁶(97-digit number)

49959736745372580909…30258939893828321279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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