Block #419,219

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2014, 10:46:28 AM · Difficulty 10.3866 · 6,375,421 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43789ac91540e261d4a325372ac69b5f5fe85a90ff65326db3006ba99c77d427

View on Chainz ↗

Height

#419,219

Difficulty

10.386613

Transactions

Size

1.07 KB

Version

Bits

0a62f911

Nonce

45,620

Timestamp

2/25/2014, 10:46:28 AM

Confirmations

6,375,421

Mined by

⛏️ P2SHANursMnYcXpHdhmJ57Qd32kLZNWzkMt9uC

Merkle Root

05c9eaa561bc89becdf527f0557b68c93f1f5be1d5472dead279e896d80f4aa0

Transactions (3)

Coinbaseaea1d584b2c222…c85ba7fd287ab6

1 in → 1 out9.2800 XPM112 B

ANursMnY…WzkMt9uC

6cfb45fe560704…53e809262a028d

1 in → 1 out2.9907 XPM192 B

ASLwqNEo…1ccEZYHV

ca3e9438f38ad3…2cd1e1d5369f44

4 in → 4 out10.3676 XPM703 B

AJ2a8S3W…tqXNT8d1 ANLfGBPm…iBuzbCuw ALvVMKLt…wbxp4TJH AeKNrjNj…1NEq95Ta

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.

2.749 × 10⁹⁸(99-digit number)

27499178479249280161…71670967575721317119

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

2.749 × 10⁹⁸(99-digit number)

27499178479249280161…71670967575721317119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.749 × 10⁹⁸(99-digit number)

27499178479249280161…71670967575721317121

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

5.499 × 10⁹⁸(99-digit number)

54998356958498560323…43341935151442634239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.499 × 10⁹⁸(99-digit number)

54998356958498560323…43341935151442634241

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

1.099 × 10⁹⁹(100-digit number)

10999671391699712064…86683870302885268479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.099 × 10⁹⁹(100-digit number)

10999671391699712064…86683870302885268481

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

2.199 × 10⁹⁹(100-digit number)

21999342783399424129…73367740605770536959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.199 × 10⁹⁹(100-digit number)

21999342783399424129…73367740605770536961

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

4.399 × 10⁹⁹(100-digit number)

43998685566798848258…46735481211541073919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.399 × 10⁹⁹(100-digit number)

43998685566798848258…46735481211541073921

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