Block #425,951

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 7:06:11 AM · Difficulty 10.3580 · 6,383,078 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c9a1d0976471509aa5e6cc81ee3128988da005eb251695ddb505ca1184204d6f

View on Chainz ↗

Height

#425,951

Difficulty

10.358003

Transactions

Size

398 B

Version

Bits

0a5ba615

Nonce

17,558

Timestamp

3/2/2014, 7:06:11 AM

Confirmations

6,383,078

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

18c9c4aa7ea23b1bd32967baf5522d719558b652abbc6f39ad70a12d8651070d

Transactions (2)

Coinbase020a3852f76502…9b5c9a28b4f7a9

1 in → 1 out9.3205 XPM110 B

AeKNrjNj…1NEq95Ta

b7fcd1ff315c9c…7903d18ed244c3

1 in → 1 out1.1200 XPM193 B

AUvmGj9D…fchFX8bk

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.

1.555 × 10¹⁰⁶(107-digit number)

15555001529551733196…13048113514008432639

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

1.555 × 10¹⁰⁶(107-digit number)

15555001529551733196…13048113514008432639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.555 × 10¹⁰⁶(107-digit number)

15555001529551733196…13048113514008432641

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

3.111 × 10¹⁰⁶(107-digit number)

31110003059103466392…26096227028016865279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.111 × 10¹⁰⁶(107-digit number)

31110003059103466392…26096227028016865281

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

6.222 × 10¹⁰⁶(107-digit number)

62220006118206932784…52192454056033730559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.222 × 10¹⁰⁶(107-digit number)

62220006118206932784…52192454056033730561

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

1.244 × 10¹⁰⁷(108-digit number)

12444001223641386556…04384908112067461119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.244 × 10¹⁰⁷(108-digit number)

12444001223641386556…04384908112067461121

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

2.488 × 10¹⁰⁷(108-digit number)

24888002447282773113…08769816224134922239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.488 × 10¹⁰⁷(108-digit number)

24888002447282773113…08769816224134922241

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 #425,951

Cookie Preferences