Block #183,527

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/28/2013, 1:58:16 AM · Difficulty 9.8580 · 6,612,313 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

739a43b6bf4b47a73a61cda69fe5621716d76690dc26a04bd12868a081876949

View on Chainz ↗

Height

#183,527

Difficulty

9.857982

Transactions

Size

734 B

Version

Bits

09dba4b1

Nonce

58,946

Timestamp

9/28/2013, 1:58:16 AM

Confirmations

6,612,313

Mined by

⛏️ P2SHAMFkKVcbthYfybM21VeAqtSFS6jCF37NqX

Merkle Root

d0191d5c9e463e3f148f196c078b55e8f8036f2e40caa5789d42c57d4093b8d5

Transactions (2)

Coinbase62fca67f877f15…30503f29a1344e

1 in → 1 out10.2800 XPM109 B

AMFkKVcb…jCF37NqX

ddd2a634f439ff…ac4532c7f2a832

4 in → 2 out41.2214 XPM536 B

ARyYtqtL…uCP66s1P AbzxW3Fi…UYE8Cog8

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.

1.784 × 10⁹³(94-digit number)

17844273421965456792…42607623568409660429

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

1.784 × 10⁹³(94-digit number)

17844273421965456792…42607623568409660429

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.784 × 10⁹³(94-digit number)

17844273421965456792…42607623568409660431

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

3.568 × 10⁹³(94-digit number)

35688546843930913585…85215247136819320859

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.568 × 10⁹³(94-digit number)

35688546843930913585…85215247136819320861

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

7.137 × 10⁹³(94-digit number)

71377093687861827171…70430494273638641719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.137 × 10⁹³(94-digit number)

71377093687861827171…70430494273638641721

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

1.427 × 10⁹⁴(95-digit number)

14275418737572365434…40860988547277283439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.427 × 10⁹⁴(95-digit number)

14275418737572365434…40860988547277283441

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

2.855 × 10⁹⁴(95-digit number)

28550837475144730868…81721977094554566879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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