Block #387,811

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/3/2014, 9:22:59 AM · Difficulty 10.4153 · 6,403,505 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

45d6775dd6d894f8669731fe308439a7f41eb6a4d9fe56b6a243078ddc801264

View on Chainz ↗

Height

#387,811

Difficulty

10.415308

Transactions

Size

431 B

Version

Bits

0a6a51a4

Nonce

17,694

Timestamp

2/3/2014, 9:22:59 AM

Confirmations

6,403,505

Merkle Root

e06351d97856cc01a5b2b9a7de11c8d5c77782047ee9b8fc21d05beb521843b7

Transactions (2)

Coinbase04b74148bcb10a…5da8d43c66c840

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

22b503d4dc36de…bced5d04606b6d

1 in → 2 out5.0352 XPM226 B

AWg9etXM…XGg7CpWE AGxMeQpn…PtE4vAxN

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.

6.749 × 10⁹²(93-digit number)

67495110810811747249…49405601680094681599

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

6.749 × 10⁹²(93-digit number)

67495110810811747249…49405601680094681599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.749 × 10⁹²(93-digit number)

67495110810811747249…49405601680094681601

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

1.349 × 10⁹³(94-digit number)

13499022162162349449…98811203360189363199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.349 × 10⁹³(94-digit number)

13499022162162349449…98811203360189363201

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

2.699 × 10⁹³(94-digit number)

26998044324324698899…97622406720378726399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.699 × 10⁹³(94-digit number)

26998044324324698899…97622406720378726401

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

5.399 × 10⁹³(94-digit number)

53996088648649397799…95244813440757452799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.399 × 10⁹³(94-digit number)

53996088648649397799…95244813440757452801

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

1.079 × 10⁹⁴(95-digit number)

10799217729729879559…90489626881514905599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.079 × 10⁹⁴(95-digit number)

10799217729729879559…90489626881514905601

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