Block #407,285

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/16/2014, 8:17:54 PM · Difficulty 10.4339 · 6,409,846 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

85b98fa5b7542aaa473c66b2a07d50fb39123c8a991c7afeba2416f6794d91c6

View on Chainz ↗

Height

#407,285

Difficulty

10.433887

Transactions

Size

1.71 KB

Version

Bits

0a6f133c

Nonce

326,121

Timestamp

2/16/2014, 8:17:54 PM

Confirmations

6,409,846

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a81c42b6206f9cb05be8f341939037ec458f663726f5da7e404757e669ac09d8

Transactions (5)

Coinbasee2813fdec1f7ca…686b15c7f41355

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

0c614e317ec032…f57742c4f0e993

4 in → 12 out36.7400 XPM874 B

AczzCoov…GHSwasZ4 AYtdXWnM…GLXsGGxq AXCBRkCb…MKXmU9ir ANL7dupX…BQ491fzW AVBgdTW6…6N4QfJBJ

4065b29a787e86…f8b1bf30645ceb

1 in → 2 out6.3074 XPM226 B

ASnigs3P…gV8V1Lfc AKgMyS1y…WoGTNrU2

c6666129fa7f8c…362c3892fa8d6d

1 in → 2 out4.0078 XPM226 B

APKaX81Y…RtYybzem AK2hELKq…m3e6XEdM

7acb5cbd8cfae6…60627134120af9

1 in → 2 out2.5800 XPM227 B

AMDDtm1q…tpqtbazE Ac24WwPt…BSeTbxUj

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.

2.883 × 10¹⁰²(103-digit number)

28837939604469331596…73646539698904391679

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

2.883 × 10¹⁰²(103-digit number)

28837939604469331596…73646539698904391679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.883 × 10¹⁰²(103-digit number)

28837939604469331596…73646539698904391681

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

5.767 × 10¹⁰²(103-digit number)

57675879208938663192…47293079397808783359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.767 × 10¹⁰²(103-digit number)

57675879208938663192…47293079397808783361

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

1.153 × 10¹⁰³(104-digit number)

11535175841787732638…94586158795617566719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.153 × 10¹⁰³(104-digit number)

11535175841787732638…94586158795617566721

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

2.307 × 10¹⁰³(104-digit number)

23070351683575465276…89172317591235133439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.307 × 10¹⁰³(104-digit number)

23070351683575465276…89172317591235133441

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

4.614 × 10¹⁰³(104-digit number)

46140703367150930553…78344635182470266879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.614 × 10¹⁰³(104-digit number)

46140703367150930553…78344635182470266881

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 #407,285

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