Block #363,006

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/17/2014, 2:48:48 AM · Difficulty 10.4149 · 6,463,493 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f067974c8ee2d578468e3d78381cb3c89dd329bbe860d6ab61a5c8e48ca8cc8a

View on Chainz ↗

Height

#363,006

Difficulty

10.414861

Transactions

Size

2.11 KB

Version

Bits

0a6a344f

Nonce

13,238

Timestamp

1/17/2014, 2:48:48 AM

Confirmations

6,463,493

Mined by

⛏️ aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

52bcdabdf5219c62d526f8b7bb2351a161d06aa9bc4c7debab537567ab26070f

Transactions (4)

Coinbase05e14df4b45fd0…965cf0ab94b2b1

1 in → 27 out9.2000 XPM981 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz AZV4TwxQ…8JnQqSoH AdaVFzHC…ivJMSTGa

b8b267adaf7594…de90c76558eabb

4 in → 1 out4.0000 XPM637 B

AMZGu8tk…XEPRnC2H

e37447cbc3900e…1e849ce5006cb9

1 in → 2 out6.2156 XPM226 B

AQnWMim4…qG8rjHWB ASrPR1mo…GPRtgEZn

cfd30f9b4c7fad…3588ebf8609558

1 in → 2 out7.2114 XPM225 B

AX4WQ8Gn…4nCZtmpL AFturLZ5…SP46gf9g

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.

2.184 × 10¹⁰³(104-digit number)

21844079333503303181…13754794927167986559

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

2.184 × 10¹⁰³(104-digit number)

21844079333503303181…13754794927167986559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.184 × 10¹⁰³(104-digit number)

21844079333503303181…13754794927167986561

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

4.368 × 10¹⁰³(104-digit number)

43688158667006606362…27509589854335973119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.368 × 10¹⁰³(104-digit number)

43688158667006606362…27509589854335973121

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

8.737 × 10¹⁰³(104-digit number)

87376317334013212724…55019179708671946239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.737 × 10¹⁰³(104-digit number)

87376317334013212724…55019179708671946241

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

1.747 × 10¹⁰⁴(105-digit number)

17475263466802642544…10038359417343892479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.747 × 10¹⁰⁴(105-digit number)

17475263466802642544…10038359417343892481

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

3.495 × 10¹⁰⁴(105-digit number)

34950526933605285089…20076718834687784959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.495 × 10¹⁰⁴(105-digit number)

34950526933605285089…20076718834687784961

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 #363,006

Cookie Preferences