Block #202,670

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/10/2013, 9:15:40 AM · Difficulty 9.8954 · 6,589,324 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8324cf1b184ae7706750b62b29902358dc47093592bb28aef9fe5a8bf2e29fbd

View on Chainz ↗

Height

#202,670

Difficulty

9.895358

Transactions

Size

1.15 KB

Version

Bits

09e5362a

Nonce

181,558

Timestamp

10/10/2013, 9:15:40 AM

Confirmations

6,589,324

Merkle Root

012af2e48932cdc806ec9423bda17051609a8901194c07e0ecfe86f00184151c

Transactions (4)

Coinbase19a4d977ae2fca…643f8c702d800a

1 in → 1 out10.2300 XPM109 B

AFxTabsk…p3rGKUD1

5efdf17174a48d…74dfd444652604

3 in → 2 out299.4460 XPM522 B

AVVuNYLQ…eC2V5avs AUxXsy7c…m5PV4bfB

97d3c25cb2e070…87a6f60f4f71e1

1 in → 2 out10.2000 XPM226 B

ASuoUi24…FwBoFbxd AQHngMrz…b9S9HgJk

5a970308976993…62ee4791725dd9

1 in → 2 out8.1805 XPM226 B

AZwWLFcK…hpMxrSND Ab5uypEx…mVqX8FmY

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.

4.620 × 10⁹⁷(98-digit number)

46202901028013371293…00452887599557708799

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

4.620 × 10⁹⁷(98-digit number)

46202901028013371293…00452887599557708799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.620 × 10⁹⁷(98-digit number)

46202901028013371293…00452887599557708801

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

9.240 × 10⁹⁷(98-digit number)

92405802056026742587…00905775199115417599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.240 × 10⁹⁷(98-digit number)

92405802056026742587…00905775199115417601

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

1.848 × 10⁹⁸(99-digit number)

18481160411205348517…01811550398230835199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.848 × 10⁹⁸(99-digit number)

18481160411205348517…01811550398230835201

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

3.696 × 10⁹⁸(99-digit number)

36962320822410697035…03623100796461670399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.696 × 10⁹⁸(99-digit number)

36962320822410697035…03623100796461670401

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

7.392 × 10⁹⁸(99-digit number)

73924641644821394070…07246201592923340799

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