Block #206,691

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/12/2013, 11:28:46 PM · Difficulty 9.9014 · 6,590,149 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

017e2a672ff9bca2516c82575599587e0602fe4e1733ee5f268d2f712fa125c7

View on Chainz ↗

Height

#206,691

Difficulty

9.901440

Transactions

Size

48.65 KB

Version

Bits

09e6c4cc

Nonce

50,233

Timestamp

10/12/2013, 11:28:46 PM

Confirmations

6,590,149

Mined by

⛏️ P2SHAGhA476zcaSiPt77cLRnhNRD8cg5xLFaaZ

Merkle Root

03145774cd729460b29ad42e3737d9f958246feab6f18f4483395a02b9bceaef

Transactions (5)

Coinbasea7d474a3e11bf9…cf9458043d6202

1 in → 1 out10.7100 XPM109 B

AGhA476z…g5xLFaaZ

3eb3aa2d402123…d15af417b02e18

1 in → 2 out8.9900 XPM225 B

APKarR6p…JERvjCZ5 AHHMo8Eg…1GTVSYgo

de44d4595484ca…1fb39f18bd5151

10 in → 2 out100.2634 XPM1.52 KB

AU8YTAuE…sKa5FD8j AVkVfMQp…CkZ8N1WB

e68850df0542cf…898c81908cd334

27 in → 2 out359.5000 XPM3.98 KB

AP5hULxg…sHU5w7fq AS3h7sid…tcWgSXoS

67fbfab52ef128…6f1407e54ad018

295 in → 2 out141.0130 XPM42.73 KB

ANqNwUfL…YR8u7wDQ AcrXkx8M…tKGb6K4t

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.

2.316 × 10⁹⁵(96-digit number)

23168416044348143565…58650586310591650379

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

2.316 × 10⁹⁵(96-digit number)

23168416044348143565…58650586310591650379

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.316 × 10⁹⁵(96-digit number)

23168416044348143565…58650586310591650381

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

4.633 × 10⁹⁵(96-digit number)

46336832088696287130…17301172621183300759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.633 × 10⁹⁵(96-digit number)

46336832088696287130…17301172621183300761

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

9.267 × 10⁹⁵(96-digit number)

92673664177392574260…34602345242366601519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.267 × 10⁹⁵(96-digit number)

92673664177392574260…34602345242366601521

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

1.853 × 10⁹⁶(97-digit number)

18534732835478514852…69204690484733203039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.853 × 10⁹⁶(97-digit number)

18534732835478514852…69204690484733203041

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

3.706 × 10⁹⁶(97-digit number)

37069465670957029704…38409380969466406079

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