Block #185,710

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 11:37:01 AM · Difficulty 9.8630 · 6,621,750 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

334a9fd5fd2a7046628fa155ed870ac44301676cb9be7eff848801b8382da266

View on Chainz ↗

Height

#185,710

Difficulty

9.863042

Transactions

Size

1.08 KB

Version

Bits

09dcf056

Nonce

60,087

Timestamp

9/29/2013, 11:37:01 AM

Confirmations

6,621,750

Mined by

⛏️ P2SHAcDoNL3woMkoVVbfWWHitidKu9ViN23bk2

Merkle Root

e1dae78c1792f32667bd9e019864559a191225aa7df323d7e9f4c6fba8054c56

Transactions (5)

Coinbase50baf68340507a…18377c704467f1

1 in → 1 out10.3000 XPM109 B

AcDoNL3w…ViN23bk2

342de14354e407…12280a8d9e7f02

1 in → 2 out10.2600 XPM226 B

AeNo3RVm…WruQcTwE AJ8j9cZj…fcbbVvCR

97d6e11689c18b…69704f2f87ce1f

1 in → 2 out10.2600 XPM227 B

AL5CC6KC…yqobBw3A AHyHEeYQ…XuELsExj

65ca972db95962…8435325aa79614

1 in → 2 out10.2600 XPM225 B

ANMHC5Rd…ctRtDowE AUfBNY3y…Mm2UYiNj

2a2901731a27dc…6a7da8c5b4076e

1 in → 2 out8.2082 XPM226 B

Abw8D7Bc…EioKVM91 AN5HJKjz…ekDi5L4q

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.

1.163 × 10⁹⁶(97-digit number)

11630503893860468561…91548070988481740799

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

1.163 × 10⁹⁶(97-digit number)

11630503893860468561…91548070988481740799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.163 × 10⁹⁶(97-digit number)

11630503893860468561…91548070988481740801

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

2.326 × 10⁹⁶(97-digit number)

23261007787720937123…83096141976963481599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.326 × 10⁹⁶(97-digit number)

23261007787720937123…83096141976963481601

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

4.652 × 10⁹⁶(97-digit number)

46522015575441874247…66192283953926963199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.652 × 10⁹⁶(97-digit number)

46522015575441874247…66192283953926963201

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

9.304 × 10⁹⁶(97-digit number)

93044031150883748494…32384567907853926399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.304 × 10⁹⁶(97-digit number)

93044031150883748494…32384567907853926401

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

1.860 × 10⁹⁷(98-digit number)

18608806230176749698…64769135815707852799

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

Block #185,710

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