Block #340,650

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2014, 10:25:38 PM · Difficulty 10.1334 · 6,468,063 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5f89e7426461443004ba1b4b4ef6b368959790bed8bfeeb09d79b13c2d7b609

View on Chainz ↗

Height

#340,650

Difficulty

10.133389

Transactions

Size

1.01 KB

Version

Bits

0a2225c2

Nonce

27,150

Timestamp

1/2/2014, 10:25:38 PM

Confirmations

6,468,063

Mined by

⛏️ 2aRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

5b6c936ae2128f4490cf6dbf62e7b7dbd99e6399c55bbb9ebd50c502e3920d9c

Transactions (1)

Coinbase5b6c936ae2128f…50c502e3920d9c

1 in → 26 out9.7200 XPM947 B

AQwRN8bE…V8PsTcY9 AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 AJzWx2VD…j4ZSMit5

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.

2.075 × 10⁹⁸(99-digit number)

20750162802420257822…04882291610803393279

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

2.075 × 10⁹⁸(99-digit number)

20750162802420257822…04882291610803393279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.075 × 10⁹⁸(99-digit number)

20750162802420257822…04882291610803393281

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

4.150 × 10⁹⁸(99-digit number)

41500325604840515644…09764583221606786559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.150 × 10⁹⁸(99-digit number)

41500325604840515644…09764583221606786561

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

8.300 × 10⁹⁸(99-digit number)

83000651209681031288…19529166443213573119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.300 × 10⁹⁸(99-digit number)

83000651209681031288…19529166443213573121

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

1.660 × 10⁹⁹(100-digit number)

16600130241936206257…39058332886427146239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.660 × 10⁹⁹(100-digit number)

16600130241936206257…39058332886427146241

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

3.320 × 10⁹⁹(100-digit number)

33200260483872412515…78116665772854292479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.320 × 10⁹⁹(100-digit number)

33200260483872412515…78116665772854292481

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

Block #340,650

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