Block #419,021

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2014, 7:46:30 AM · Difficulty 10.3843 · 6,391,136 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70dba7a775d9d8ddf84b06793eb1a154e06e1391994aaa6fde1a952e0a44c279

View on Chainz ↗

Height

#419,021

Difficulty

10.384274

Transactions

Size

1.26 KB

Version

Bits

0a625fcc

Nonce

14,405

Timestamp

2/25/2014, 7:46:30 AM

Confirmations

6,391,136

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2bfbc17082bae6e727a3582ed748b17a9ff6984ca3e839955cf8b1f668689c2e

Transactions (2)

Coinbaseef32f778f9f28e…e70c1d904b5475

1 in → 1 out9.2800 XPM110 B

AeKNrjNj…1NEq95Ta

1c82b1cd82cf64…79d5ec26d255b0

5 in → 15 out46.1400 XPM1.06 KB

AXYs2oWF…yofeFV1T AHu4i1fi…2yxd2rEX AWKJw4CW…t8uGdGtR AMUk2TKR…wfJamBdD AL6hfYqf…jYfKt9LA

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.

4.271 × 10¹⁰³(104-digit number)

42717673035173188231…54440732061310852849

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

4.271 × 10¹⁰³(104-digit number)

42717673035173188231…54440732061310852849

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.271 × 10¹⁰³(104-digit number)

42717673035173188231…54440732061310852851

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

8.543 × 10¹⁰³(104-digit number)

85435346070346376463…08881464122621705699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.543 × 10¹⁰³(104-digit number)

85435346070346376463…08881464122621705701

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

1.708 × 10¹⁰⁴(105-digit number)

17087069214069275292…17762928245243411399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.708 × 10¹⁰⁴(105-digit number)

17087069214069275292…17762928245243411401

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

3.417 × 10¹⁰⁴(105-digit number)

34174138428138550585…35525856490486822799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.417 × 10¹⁰⁴(105-digit number)

34174138428138550585…35525856490486822801

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

6.834 × 10¹⁰⁴(105-digit number)

68348276856277101170…71051712980973645599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.834 × 10¹⁰⁴(105-digit number)

68348276856277101170…71051712980973645601

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 #419,021

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