Block #384,288

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/1/2014, 12:07:07 AM · Difficulty 10.4016 · 6,432,889 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6246f0afb76e9fb272d1814e94a8489a7ebc592a632172f9bea8a1b1c5a4f07b

View on Chainz ↗

Height

#384,288

Difficulty

10.401631

Transactions

Size

1.09 KB

Version

Bits

0a66d14e

Nonce

16,780,809

Timestamp

2/1/2014, 12:07:07 AM

Confirmations

6,432,889

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ce3b9ee6f322883f664dd217ae760eb1870a3c41d0de2261303dcdc0e324e8c7

Transactions (5)

Coinbaseb706d58b424aa3…aa1141251ebf4e

1 in → 1 out9.2700 XPM116 B

AbwWkWZt…kawDhufa

bc74e512aa77ed…edef2cdf66df33

1 in → 2 out7.1660 XPM226 B

ARi3o4K9…sJKTPJVT AMdyVZfN…BoRYvibU

b7b3af1bd36a12…4940b0eb0712c2

1 in → 2 out5.1276 XPM226 B

AetMuNgb…n2wdbLdd Af6MkJWT…xAzxqSm5

b09e6a936c89cf…67e1a64e558d0f

1 in → 2 out7.1644 XPM227 B

ASD9boJL…zq5Ye1Ah AMSESxoW…jJHGdLGw

2fcd137b12cb83…e3209390130412

1 in → 2 out5.1366 XPM227 B

AGusNSbi…TMhj3ShN ARpSeuju…QmronKxc

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.

8.665 × 10⁹⁵(96-digit number)

86652466823814227711…03728416694688274559

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

8.665 × 10⁹⁵(96-digit number)

86652466823814227711…03728416694688274559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.665 × 10⁹⁵(96-digit number)

86652466823814227711…03728416694688274561

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

1.733 × 10⁹⁶(97-digit number)

17330493364762845542…07456833389376549119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.733 × 10⁹⁶(97-digit number)

17330493364762845542…07456833389376549121

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

3.466 × 10⁹⁶(97-digit number)

34660986729525691084…14913666778753098239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.466 × 10⁹⁶(97-digit number)

34660986729525691084…14913666778753098241

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

6.932 × 10⁹⁶(97-digit number)

69321973459051382169…29827333557506196479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.932 × 10⁹⁶(97-digit number)

69321973459051382169…29827333557506196481

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

1.386 × 10⁹⁷(98-digit number)

13864394691810276433…59654667115012392959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.386 × 10⁹⁷(98-digit number)

13864394691810276433…59654667115012392961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.772 × 10⁹⁷(98-digit number)

27728789383620552867…19309334230024785919

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #384,288

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