Block #343,760

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/4/2014, 9:14:52 PM · Difficulty 10.1845 · 6,451,120 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

01b8cf082192d28b5a54bdb156caa654063ac71f24ccfcdbe6225c20a288f96e

View on Chainz ↗

Height

#343,760

Difficulty

10.184510

Transactions

Size

1.58 KB

Version

Bits

0a2f3c0b

Nonce

23,323

Timestamp

1/4/2014, 9:14:52 PM

Confirmations

6,451,120

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

96714a368d4396b6798bf2ac158cae401f2b6378f122e8f66e7124dafe038701

Transactions (4)

Coinbasea32454efd2a4ca…b484ba38f1dd18

1 in → 1 out9.6600 XPM110 B

AeKNrjNj…1NEq95Ta

3b7ff80a72c16f…65e618689daebe

1 in → 2 out8619.3528 XPM226 B

AamQHajr…m1B5N2sL AJLHU8oH…L5BnGfhG

2c8836216c0d80…3065872a5690fd

5 in → 2 out500.0100 XPM818 B

AMGhfwhS…REEKpcnw AJjnK9uC…VreFquR4

948805dd52c331…23e8fd671c4a45

2 in → 2 out2.6508 XPM375 B

APfPQsqu…NBoZCRug ALVMsfjq…GPnskiJz

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.

2.176 × 10⁹⁹(100-digit number)

21768613250660018501…25554226681265704959

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

2.176 × 10⁹⁹(100-digit number)

21768613250660018501…25554226681265704959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.176 × 10⁹⁹(100-digit number)

21768613250660018501…25554226681265704961

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

4.353 × 10⁹⁹(100-digit number)

43537226501320037002…51108453362531409919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.353 × 10⁹⁹(100-digit number)

43537226501320037002…51108453362531409921

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

8.707 × 10⁹⁹(100-digit number)

87074453002640074005…02216906725062819839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.707 × 10⁹⁹(100-digit number)

87074453002640074005…02216906725062819841

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

1.741 × 10¹⁰⁰(101-digit number)

17414890600528014801…04433813450125639679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.741 × 10¹⁰⁰(101-digit number)

17414890600528014801…04433813450125639681

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

3.482 × 10¹⁰⁰(101-digit number)

34829781201056029602…08867626900251279359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.482 × 10¹⁰⁰(101-digit number)

34829781201056029602…08867626900251279361

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