Block #199,492

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/8/2013, 10:06:48 AM · Difficulty 9.8876 · 6,595,256 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb97954b1715f16b1156a1f1f75b91a7004606bbf9d15a5227fed1d303a2529e

View on Chainz ↗

Height

#199,492

Difficulty

9.887593

Transactions

Size

1.28 KB

Version

Bits

09e33948

Nonce

70,456

Timestamp

10/8/2013, 10:06:48 AM

Confirmations

6,595,256

Mined by

⛏️ P2SHAM2vrwSSvJgXzt8ghnje8Wh3xGAfbCGwrh

Merkle Root

ffb7da49e83d29d7f3c91567e171c984b4afa0bd1b14046b2da02dd81dc5e535

Transactions (2)

Coinbasedc736f981e9c8e…e1dd69f677d9fa

1 in → 1 out10.2300 XPM109 B

AM2vrwSS…AfbCGwrh

44c26df6562803…f8327724ceadeb

7 in → 2 out279.9089 XPM1.09 KB

AZ3F2bZw…4WFdna9z AKPsK7hq…JimrEcdU

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.

3.461 × 10⁹⁸(99-digit number)

34612576149609506043…36492182788396247819

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

3.461 × 10⁹⁸(99-digit number)

34612576149609506043…36492182788396247819

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.461 × 10⁹⁸(99-digit number)

34612576149609506043…36492182788396247821

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

6.922 × 10⁹⁸(99-digit number)

69225152299219012086…72984365576792495639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.922 × 10⁹⁸(99-digit number)

69225152299219012086…72984365576792495641

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

1.384 × 10⁹⁹(100-digit number)

13845030459843802417…45968731153584991279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.384 × 10⁹⁹(100-digit number)

13845030459843802417…45968731153584991281

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

2.769 × 10⁹⁹(100-digit number)

27690060919687604834…91937462307169982559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.769 × 10⁹⁹(100-digit number)

27690060919687604834…91937462307169982561

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

5.538 × 10⁹⁹(100-digit number)

55380121839375209669…83874924614339965119

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