Block #39,386

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 1:25:16 PM · Difficulty 8.3126 · 6,755,391 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c280e781f543c2bd8d1a411b3492a1ae13629236e7a671d7a4e7425eb03a5d43

View on Chainz ↗

Height

#39,386

Difficulty

8.312591

Transactions

Size

3.83 KB

Version

Bits

085005f2

Nonce

157

Timestamp

7/14/2013, 1:25:16 PM

Confirmations

6,755,391

Mined by

⛏️ P2SHAPc6qChA1xf9vUduf2vmVCrPvFLNJfEiDV

Merkle Root

4bcc10cc3b53e1ccf75ad709116c6ba9bbd70b9eee03fca9caa46f05ed131a44

Transactions (2)

Coinbase0d021e4adfe761…e40fb18db9850b

1 in → 1 out14.4900 XPM110 B

APc6qChA…LNJfEiDV

0081fa86536269…f067c04d9562f6

32 in → 2 out500.4900 XPM3.64 KB

AXPZNYtB…aa11TsRu AWThhUX5…uhd1H2jp

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.

1.639 × 10⁹⁸(99-digit number)

16396637781242364802…25486929622499598159

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

1.639 × 10⁹⁸(99-digit number)

16396637781242364802…25486929622499598159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.639 × 10⁹⁸(99-digit number)

16396637781242364802…25486929622499598161

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

3.279 × 10⁹⁸(99-digit number)

32793275562484729605…50973859244999196319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.279 × 10⁹⁸(99-digit number)

32793275562484729605…50973859244999196321

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

6.558 × 10⁹⁸(99-digit number)

65586551124969459210…01947718489998392639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.558 × 10⁹⁸(99-digit number)

65586551124969459210…01947718489998392641

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

1.311 × 10⁹⁹(100-digit number)

13117310224993891842…03895436979996785279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.311 × 10⁹⁹(100-digit number)

13117310224993891842…03895436979996785281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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