Block #327,008

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/24/2013, 6:05:10 AM · Difficulty 10.1784 · 6,485,929 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e71db1aa206b94bbcdfbbca70bb2ed7f84542f6641058d058611f0bd58ae086d

View on Chainz ↗

Height

#327,008

Difficulty

10.178441

Transactions

Size

1.20 KB

Version

Bits

0a2dae55

Nonce

86,185

Timestamp

12/24/2013, 6:05:10 AM

Confirmations

6,485,929

Mined by

⛏️ `aR$AGpcvDeigYqHqmdkp8xXGcaghW96H8hx8F

Merkle Root

42e25db8f6d343722ae854e958134dbe3b63ba732651f4807d2a52f6caa8f31a

Transactions (2)

Coinbase618a1c6e6fb926…6c4c5331747554

1 in → 25 out9.6400 XPM913 B

AGpcvDei…96H8hx8F AYvn1vnk…fpKFDjfh AJdLNXdT…prit4boi Aac9Hjdg…P4ktypc3 AQjgN2dS…uEQws1Mu

01d610ec1f17c9…156fb0ad4be259

1 in → 2 out2.3817 XPM226 B

AQv2CsCc…7ntrpzGa AUyx6Zc2…aZPWCMTP

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.

1.047 × 10¹⁰²(103-digit number)

10470278127418328575…09797519391942119259

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

1.047 × 10¹⁰²(103-digit number)

10470278127418328575…09797519391942119259

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.047 × 10¹⁰²(103-digit number)

10470278127418328575…09797519391942119261

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

2.094 × 10¹⁰²(103-digit number)

20940556254836657151…19595038783884238519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.094 × 10¹⁰²(103-digit number)

20940556254836657151…19595038783884238521

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

4.188 × 10¹⁰²(103-digit number)

41881112509673314303…39190077567768477039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.188 × 10¹⁰²(103-digit number)

41881112509673314303…39190077567768477041

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

8.376 × 10¹⁰²(103-digit number)

83762225019346628607…78380155135536954079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.376 × 10¹⁰²(103-digit number)

83762225019346628607…78380155135536954081

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

1.675 × 10¹⁰³(104-digit number)

16752445003869325721…56760310271073908159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.675 × 10¹⁰³(104-digit number)

16752445003869325721…56760310271073908161

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 #327,008

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