Block #325,291

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/22/2013, 10:34:50 PM · Difficulty 10.2074 · 6,477,376 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6188a5689771db17ada9e91db99c95ff2ad277db7f1e054ba80ff49d6d37ede5

View on Chainz ↗

Height

#325,291

Difficulty

10.207423

Transactions

Size

4.11 KB

Version

Bits

0a3519a7

Nonce

7,748

Timestamp

12/22/2013, 10:34:50 PM

Confirmations

6,477,376

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

4cf607cd0fb49e4576aa227259b288214fd24bfeec89f6175b2fd18feb2225f8

Transactions (3)

Coinbasee9c74b34c1992e…de186741a5953f

1 in → 1 out9.6300 XPM110 B

AeKNrjNj…1NEq95Ta

649f55cf058f50…0104eb7f918137

25 in → 2 out8.2763 XPM3.69 KB

ASevHL4h…D33M414o AXV1oPfC…UejBS3k1

166b1458f286b2…118a4cbe005781

1 in → 2 out1.1640 XPM226 B

AUESZFBt…Qys1S77m AdgmqJRT…xfd5jWGs

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.

1.216 × 10¹⁰⁰(101-digit number)

12165427898958768691…83506917172624144669

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

1.216 × 10¹⁰⁰(101-digit number)

12165427898958768691…83506917172624144669

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.216 × 10¹⁰⁰(101-digit number)

12165427898958768691…83506917172624144671

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

2.433 × 10¹⁰⁰(101-digit number)

24330855797917537382…67013834345248289339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.433 × 10¹⁰⁰(101-digit number)

24330855797917537382…67013834345248289341

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

4.866 × 10¹⁰⁰(101-digit number)

48661711595835074764…34027668690496578679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.866 × 10¹⁰⁰(101-digit number)

48661711595835074764…34027668690496578681

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

9.732 × 10¹⁰⁰(101-digit number)

97323423191670149528…68055337380993157359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.732 × 10¹⁰⁰(101-digit number)

97323423191670149528…68055337380993157361

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

1.946 × 10¹⁰¹(102-digit number)

19464684638334029905…36110674761986314719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.946 × 10¹⁰¹(102-digit number)

19464684638334029905…36110674761986314721

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