Block #200,005

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/8/2013, 6:04:16 PM · Difficulty 9.8884 · 6,608,986 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa0d6aeffbb3711a2878495b2a324bf9cfc9b2d5fe63e8ffbc8e340d4715cd68

View on Chainz ↗

Height

#200,005

Difficulty

9.888394

Transactions

Size

1.60 KB

Version

Bits

09e36dcd

Nonce

14,881

Timestamp

10/8/2013, 6:04:16 PM

Confirmations

6,608,986

Mined by

⛏️ P2SHAekpAPojkqQWMQEgQSb8s39KPLB2jiw1sN

Merkle Root

90b11cd7463b8eddc0bef9996df8c55ba94ce487c6cc6bfd47eefdc2bd0ccd4b

Transactions (4)

Coinbase9a820641435be3…99d22a596d0b92

1 in → 1 out10.2400 XPM109 B

AekpAPoj…B2jiw1sN

a5ab3030a81778…b1f9024851b238

3 in → 6 out19.6228 XPM624 B

APD3nnZi…CZSB6uxy AQXUSoBL…CzbjKp8b APd3tden…qhRE2ARG AHADV2Ly…7mcKNDYV ANvtpRa1…QjsraDJz

97fd4341e45cc6…d0f8a1e205a2b0

3 in → 5 out12.7251 XPM591 B

ANxERLYc…v7fC1vqc AcyPVp7N…dDULWcdA Ac5sZcdP…kzV4eckG AdSKb2ue…gskipCSD ANvtpRa1…QjsraDJz

3ead2e1f33fb97…244f6a5e7c484c

1 in → 2 out7.1297 XPM225 B

AXtUHczo…Ke72YFw4 AcADmAoe…8iNnoMzB

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.

2.017 × 10¹⁰²(103-digit number)

20178939258071741457…36476881900833136639

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

2.017 × 10¹⁰²(103-digit number)

20178939258071741457…36476881900833136639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.017 × 10¹⁰²(103-digit number)

20178939258071741457…36476881900833136641

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

4.035 × 10¹⁰²(103-digit number)

40357878516143482914…72953763801666273279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.035 × 10¹⁰²(103-digit number)

40357878516143482914…72953763801666273281

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

8.071 × 10¹⁰²(103-digit number)

80715757032286965828…45907527603332546559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.071 × 10¹⁰²(103-digit number)

80715757032286965828…45907527603332546561

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

1.614 × 10¹⁰³(104-digit number)

16143151406457393165…91815055206665093119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.614 × 10¹⁰³(104-digit number)

16143151406457393165…91815055206665093121

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

3.228 × 10¹⁰³(104-digit number)

32286302812914786331…83630110413330186239

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 #200,005

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