Block #430,402

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/5/2014, 11:44:53 AM · Difficulty 10.3423 · 6,372,593 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6664040d05ebb854fff304df98587875c76a3a58b56e00bb7fecdca525681fb5

View on Chainz ↗

Height

#430,402

Difficulty

10.342292

Transactions

Size

394 B

Version

Bits

0a57a077

Nonce

14,848

Timestamp

3/5/2014, 11:44:53 AM

Confirmations

6,372,593

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

ee897fd6382f14e806c8663d5c7286eb3533eafd9862c1aabf9a0ea549407d4f

Transactions (2)

Coinbaseff2c1c5fb0bcd7…eb0fe5866343ab

1 in → 1 out9.3482 XPM110 B

AeKNrjNj…1NEq95Ta

5b36109f8d3ed4…b4bad6a46628d9

1 in → 1 out1.4300 XPM192 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.

1.392 × 10¹⁰⁰(101-digit number)

13923256629483461343…31866578229719577599

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

1.392 × 10¹⁰⁰(101-digit number)

13923256629483461343…31866578229719577599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.392 × 10¹⁰⁰(101-digit number)

13923256629483461343…31866578229719577601

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

2.784 × 10¹⁰⁰(101-digit number)

27846513258966922686…63733156459439155199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.784 × 10¹⁰⁰(101-digit number)

27846513258966922686…63733156459439155201

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

5.569 × 10¹⁰⁰(101-digit number)

55693026517933845372…27466312918878310399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.569 × 10¹⁰⁰(101-digit number)

55693026517933845372…27466312918878310401

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

1.113 × 10¹⁰¹(102-digit number)

11138605303586769074…54932625837756620799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.113 × 10¹⁰¹(102-digit number)

11138605303586769074…54932625837756620801

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

2.227 × 10¹⁰¹(102-digit number)

22277210607173538148…09865251675513241599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.227 × 10¹⁰¹(102-digit number)

22277210607173538148…09865251675513241601

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