Block #423,335

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/28/2014, 9:43:42 AM · Difficulty 10.3706 · 6,385,639 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

424b9dda3f943d68992c589d521042ba962c4cc5336c2c78c64ef1b1c7fc5f2e

View on Chainz ↗

Height

#423,335

Difficulty

10.370588

Transactions

Size

393 B

Version

Bits

0a5edee0

Nonce

15,886

Timestamp

2/28/2014, 9:43:42 AM

Confirmations

6,385,639

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a239d3fcf23b5b61be8225fb608231865327e01f90f6d86d42ce3b32fbbd6be7

Transactions (2)

Coinbase53cd25bc995516…7cd8dc4aa27281

1 in → 1 out9.2900 XPM110 B

AeKNrjNj…1NEq95Ta

c05f28be479ed1…a08b5489c67c79

1 in → 2 out9.2200 XPM192 B

AbxSPrXb…vS4n2Ueh AYKVeNA9…BbJrTDhi

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.

2.170 × 10⁹⁶(97-digit number)

21701352592143255513…04384861009562305599

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

2.170 × 10⁹⁶(97-digit number)

21701352592143255513…04384861009562305599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.170 × 10⁹⁶(97-digit number)

21701352592143255513…04384861009562305601

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

4.340 × 10⁹⁶(97-digit number)

43402705184286511027…08769722019124611199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.340 × 10⁹⁶(97-digit number)

43402705184286511027…08769722019124611201

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

8.680 × 10⁹⁶(97-digit number)

86805410368573022054…17539444038249222399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.680 × 10⁹⁶(97-digit number)

86805410368573022054…17539444038249222401

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

1.736 × 10⁹⁷(98-digit number)

17361082073714604410…35078888076498444799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.736 × 10⁹⁷(98-digit number)

17361082073714604410…35078888076498444801

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

3.472 × 10⁹⁷(98-digit number)

34722164147429208821…70157776152996889599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.472 × 10⁹⁷(98-digit number)

34722164147429208821…70157776152996889601

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 #423,335

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