Block #404,211

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/14/2014, 4:39:03 PM · Difficulty 10.4350 · 6,403,818 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bdad4b168986ad1908509e548f97ac6d8cfc5eac47c592fa60a635c2754a9ed3

View on Chainz ↗

Height

#404,211

Difficulty

10.435016

Transactions

Size

970 B

Version

Bits

0a6f5d36

Nonce

25,831

Timestamp

2/14/2014, 4:39:03 PM

Confirmations

6,403,818

Mined by

⛏️ *aRFAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f5acc61a3c3af36891aa60c240fe195c4c01c1ac0c13085ba0b6b8daf05aa801

Transactions (1)

Coinbasef5acc61a3c3af3…b6b8daf05aa801

1 in → 24 out9.1700 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

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.

5.575 × 10⁹⁷(98-digit number)

55756667463490439504…39473068181678095359

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

5.575 × 10⁹⁷(98-digit number)

55756667463490439504…39473068181678095359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.575 × 10⁹⁷(98-digit number)

55756667463490439504…39473068181678095361

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

1.115 × 10⁹⁸(99-digit number)

11151333492698087900…78946136363356190719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.115 × 10⁹⁸(99-digit number)

11151333492698087900…78946136363356190721

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

2.230 × 10⁹⁸(99-digit number)

22302666985396175801…57892272726712381439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.230 × 10⁹⁸(99-digit number)

22302666985396175801…57892272726712381441

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

4.460 × 10⁹⁸(99-digit number)

44605333970792351603…15784545453424762879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.460 × 10⁹⁸(99-digit number)

44605333970792351603…15784545453424762881

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

8.921 × 10⁹⁸(99-digit number)

89210667941584703206…31569090906849525759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.921 × 10⁹⁸(99-digit number)

89210667941584703206…31569090906849525761

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 #404,211

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