Block #196,357

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/6/2013, 10:42:39 AM · Difficulty 9.8807 · 6,599,620 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f0d00bc46f46d48d2486461c1939e5bd3bf4f077e2e6f776f27a8f188490473e

View on Chainz ↗

Height

#196,357

Difficulty

9.880713

Transactions

Size

2.59 KB

Version

Bits

09e17670

Nonce

72,254

Timestamp

10/6/2013, 10:42:39 AM

Confirmations

6,599,620

Mined by

⛏️ P2SHAeLjYwoNEtegS2appumCvfLvBtqGBxBQFd

Merkle Root

a342c3c6e4749c42ea4a0845456589ac62eabc43e87c577e1103018b3471eb17

Transactions (4)

Coinbase1730f013bdd317…1a5fc1a148fc2a

1 in → 1 out10.2700 XPM109 B

AeLjYwoN…qGBxBQFd

05c41cbddf6bc0…a26add214739a7

9 in → 2 out10.0103 XPM1.37 KB

AdeeJkQ1…Dhe29gvF AW5uftew…xtaz9fHJ

f8384a9cb74423…61966887ce5d57

1 in → 2 out5.0637 XPM227 B

Abv7T9f6…KHfYi4jT AMqy1Z9q…9qLErWJg

e09bcd56382d2b…3c0f6b8500d935

5 in → 2 out2.0134 XPM818 B

AQEjgvVa…AnDqsEDF AdbC5fHj…YSFywdtY

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.

1.304 × 10⁹⁰(91-digit number)

13045643628439918533…17298052235883386709

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

1.304 × 10⁹⁰(91-digit number)

13045643628439918533…17298052235883386709

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.304 × 10⁹⁰(91-digit number)

13045643628439918533…17298052235883386711

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

2.609 × 10⁹⁰(91-digit number)

26091287256879837067…34596104471766773419

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.609 × 10⁹⁰(91-digit number)

26091287256879837067…34596104471766773421

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

5.218 × 10⁹⁰(91-digit number)

52182574513759674134…69192208943533546839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.218 × 10⁹⁰(91-digit number)

52182574513759674134…69192208943533546841

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

1.043 × 10⁹¹(92-digit number)

10436514902751934826…38384417887067093679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.043 × 10⁹¹(92-digit number)

10436514902751934826…38384417887067093681

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

2.087 × 10⁹¹(92-digit number)

20873029805503869653…76768835774134187359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.087 × 10⁹¹(92-digit number)

20873029805503869653…76768835774134187361

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