Block #402,681

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2014, 2:47:49 PM · Difficulty 10.4368 · 6,410,012 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

343be7b853243957879dfa54e78456593f9f8f66e2d51d12b3ff81410334255b

View on Chainz ↗

Height

#402,681

Difficulty

10.436848

Transactions

Size

2.01 KB

Version

Bits

0a6fd54c

Nonce

222,435

Timestamp

2/13/2014, 2:47:49 PM

Confirmations

6,410,012

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

1f65ecac9e453a65a2b0d01dd9656b1cd0bcff1602426298833ab3ece511c909

Transactions (2)

Coinbase21152052fb6eac…3ed52bcb5bcbb2

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

ddbfa2c3507c6d…5c29ab7b126645

12 in → 2 out36.0571 XPM1.81 KB

AWerYQST…AQ8sYmpE ASFRopuH…FjkWU1AZ

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.

2.362 × 10⁹⁷(98-digit number)

23620941416396927001…67356290525683722539

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

2.362 × 10⁹⁷(98-digit number)

23620941416396927001…67356290525683722539

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.362 × 10⁹⁷(98-digit number)

23620941416396927001…67356290525683722541

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

4.724 × 10⁹⁷(98-digit number)

47241882832793854002…34712581051367445079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.724 × 10⁹⁷(98-digit number)

47241882832793854002…34712581051367445081

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

9.448 × 10⁹⁷(98-digit number)

94483765665587708005…69425162102734890159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.448 × 10⁹⁷(98-digit number)

94483765665587708005…69425162102734890161

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

1.889 × 10⁹⁸(99-digit number)

18896753133117541601…38850324205469780319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.889 × 10⁹⁸(99-digit number)

18896753133117541601…38850324205469780321

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

3.779 × 10⁹⁸(99-digit number)

37793506266235083202…77700648410939560639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.779 × 10⁹⁸(99-digit number)

37793506266235083202…77700648410939560641

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 #402,681

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