Block #408,471

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2014, 4:30:38 PM · Difficulty 10.4313 · 6,401,466 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2faf8903f314434ccd042415a2fc40b2a95db60a3e6dec20fd0889bcd59d440a

View on Chainz ↗

Height

#408,471

Difficulty

10.431299

Transactions

Size

1.65 KB

Version

Bits

0a6e6998

Nonce

77,892

Timestamp

2/17/2014, 4:30:38 PM

Confirmations

6,401,466

Mined by

⛏️ P2SHATThMXEkuCK5mRjTzuMkQAWkALoLe4GAcR

Merkle Root

decab0045a32e1f34c50a2501a257e8c8dcf8953d89c0e9200e0422cbebc99aa

Transactions (4)

Coinbased87e41d6704770…b1ff3a1c903df7

1 in → 1 out9.2100 XPM109 B

ATThMXEk…oLe4GAcR

9e5facb2990120…a0784f1a1308e6

1 in → 1 out9.1800 XPM158 B

AbP1iY2S…QXTtEVYb

849bf6950d1edb…5d93f9be3176bc

3 in → 9 out27.8700 XPM659 B

AXPoV6wH…1Hot5hv9 AcRJhPSS…rM6dyn1m ATz1Sryu…PWZHWKYx AQ1R6V2e…Ch7Bdubb AHrFNmf8…hpqU2WtU

c0c67a416571be…b5800ba8c86e92

4 in → 2 out4.0151 XPM672 B

ASYDzXXq…MRQa5KvC AapHn8m6…7Xjjxdyr

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.

3.776 × 10⁹⁹(100-digit number)

37761666876324820484…33336377396653757279

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

3.776 × 10⁹⁹(100-digit number)

37761666876324820484…33336377396653757279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.776 × 10⁹⁹(100-digit number)

37761666876324820484…33336377396653757281

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

7.552 × 10⁹⁹(100-digit number)

75523333752649640969…66672754793307514559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.552 × 10⁹⁹(100-digit number)

75523333752649640969…66672754793307514561

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

1.510 × 10¹⁰⁰(101-digit number)

15104666750529928193…33345509586615029119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.510 × 10¹⁰⁰(101-digit number)

15104666750529928193…33345509586615029121

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

3.020 × 10¹⁰⁰(101-digit number)

30209333501059856387…66691019173230058239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.020 × 10¹⁰⁰(101-digit number)

30209333501059856387…66691019173230058241

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

6.041 × 10¹⁰⁰(101-digit number)

60418667002119712775…33382038346460116479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.041 × 10¹⁰⁰(101-digit number)

60418667002119712775…33382038346460116481

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 #408,471

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