Block #386,947

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/2/2014, 7:17:44 PM · Difficulty 10.4130 · 6,420,659 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

71e7ac8748630ef2f854b206bce37d588d5e37a0ccee2082306d15656651c7e1

View on Chainz ↗

Height

#386,947

Difficulty

10.412959

Transactions

Size

1.59 KB

Version

Bits

0a69b7ac

Nonce

67,691

Timestamp

2/2/2014, 7:17:44 PM

Confirmations

6,420,659

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

7bd24b4db128e584c5a5ae765ec021977dc19776f9b0e79a354b86c74afa39df

Transactions (2)

Coinbase5854a5c0d84639…a3879c28bf2477

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

8fb2e71a67fd6f…5a71886d09942e

8 in → 10 out28.3607 XPM1.40 KB

AQmbZZK2…8Hh6ZeM7 AWvUeQTE…6gtdWqxv ATqL92FR…hv5XHEu1 AZwXBq4j…rzStTzBk AeKNrjNj…1NEq95Ta

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.

1.044 × 10⁹³(94-digit number)

10449194766188814844…14992867693134847999

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

1.044 × 10⁹³(94-digit number)

10449194766188814844…14992867693134847999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.044 × 10⁹³(94-digit number)

10449194766188814844…14992867693134848001

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

2.089 × 10⁹³(94-digit number)

20898389532377629689…29985735386269695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.089 × 10⁹³(94-digit number)

20898389532377629689…29985735386269696001

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

4.179 × 10⁹³(94-digit number)

41796779064755259378…59971470772539391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.179 × 10⁹³(94-digit number)

41796779064755259378…59971470772539392001

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

8.359 × 10⁹³(94-digit number)

83593558129510518757…19942941545078783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.359 × 10⁹³(94-digit number)

83593558129510518757…19942941545078784001

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

1.671 × 10⁹⁴(95-digit number)

16718711625902103751…39885883090157567999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.671 × 10⁹⁴(95-digit number)

16718711625902103751…39885883090157568001

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 #386,947

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