Block #196,638

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/6/2013, 3:16:49 PM · Difficulty 9.8809 · 6,598,410 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

968229738be81200d7ed81a5a2aaeac6688104ed3065e5e6ac5a7b643f0f1199

View on Chainz ↗

Height

#196,638

Difficulty

9.880887

Transactions

Size

457 B

Version

Bits

09e181cf

Nonce

114,103

Timestamp

10/6/2013, 3:16:49 PM

Confirmations

6,598,410

Mined by

⛏️ P2SHATyFBW7VF8kqYDVLUXDZkeeiDUHWJYE6j8

Merkle Root

5baf05189e8c5080d8ca0d8b2323587f6299803a69c62badfc15af40afcfe6c6

Transactions (2)

Coinbase237d812695030a…163a0013ce533f

1 in → 1 out10.2400 XPM109 B

ATyFBW7V…HWJYE6j8

4adb50acae4e59…c288ff37ba9bb0

1 in → 4 out10.2300 XPM259 B

ANAVEjQm…6wqP126u AQXUSoBL…CzbjKp8b ANvtpRa1…QjsraDJz ALVaS9Pa…WUbnL1Gt

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.

4.317 × 10⁹¹(92-digit number)

43170802067202879498…20739338627360290159

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

4.317 × 10⁹¹(92-digit number)

43170802067202879498…20739338627360290159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.317 × 10⁹¹(92-digit number)

43170802067202879498…20739338627360290161

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

8.634 × 10⁹¹(92-digit number)

86341604134405758997…41478677254720580319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.634 × 10⁹¹(92-digit number)

86341604134405758997…41478677254720580321

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

1.726 × 10⁹²(93-digit number)

17268320826881151799…82957354509441160639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.726 × 10⁹²(93-digit number)

17268320826881151799…82957354509441160641

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

3.453 × 10⁹²(93-digit number)

34536641653762303598…65914709018882321279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.453 × 10⁹²(93-digit number)

34536641653762303598…65914709018882321281

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

6.907 × 10⁹²(93-digit number)

69073283307524607197…31829418037764642559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.907 × 10⁹²(93-digit number)

69073283307524607197…31829418037764642561

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