Block #392,678

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/6/2014, 3:04:33 PM · Difficulty 10.4401 · 6,413,942 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b67656f8c2c5cd8642a65df2df212fd94c1eb2ae87878a3603664698ca91a9fe

View on Chainz ↗

Height

#392,678

Difficulty

10.440149

Transactions

Size

1.08 KB

Version

Bits

0a70ad9a

Nonce

160,191

Timestamp

2/6/2014, 3:04:33 PM

Confirmations

6,413,942

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

dd1fc13d9a4b401a3d34feb955bd8c575f68925497cb4ef37436a975b663af76

Transactions (5)

Coinbase8669d77f97145e…b7ece8da6cbd60

1 in → 1 out9.2000 XPM110 B

AeKNrjNj…1NEq95Ta

e6daba191551b1…1aa54abe0833c7

1 in → 2 out4.4900 XPM227 B

AGDkDqRp…j69DdPrk AZfJe62i…zCagiMk6

db0016091b4ad0…07fbc35fbda7bc

1 in → 2 out2.0781 XPM225 B

AHg1i3CQ…jcKctFwV ASJxJS8q…rSrFoTLt

74b3e2610a76c4…800bdeed95a272

1 in → 2 out3.2455 XPM226 B

AawixgFr…3Cd95Uu2 ASPHSrmw…dPdmjjjs

74dc91130dbd78…dc9b56d19605eb

1 in → 2 out3.1016 XPM227 B

AVURx48p…9BpJc8ru AP4iambd…watkz3eK

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.

2.657 × 10⁹⁹(100-digit number)

26573639700513786474…19330486626594521359

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

2.657 × 10⁹⁹(100-digit number)

26573639700513786474…19330486626594521359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.657 × 10⁹⁹(100-digit number)

26573639700513786474…19330486626594521361

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

5.314 × 10⁹⁹(100-digit number)

53147279401027572948…38660973253189042719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.314 × 10⁹⁹(100-digit number)

53147279401027572948…38660973253189042721

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

1.062 × 10¹⁰⁰(101-digit number)

10629455880205514589…77321946506378085439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.062 × 10¹⁰⁰(101-digit number)

10629455880205514589…77321946506378085441

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

2.125 × 10¹⁰⁰(101-digit number)

21258911760411029179…54643893012756170879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.125 × 10¹⁰⁰(101-digit number)

21258911760411029179…54643893012756170881

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

4.251 × 10¹⁰⁰(101-digit number)

42517823520822058358…09287786025512341759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.251 × 10¹⁰⁰(101-digit number)

42517823520822058358…09287786025512341761

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 #392,678

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