Block #208,242

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 9:55:51 PM · Difficulty 9.9054 · 6,587,165 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9f3d67f3701ed4936430bc5f20ff854f66f51c5c123c76cd85691511778352f8

View on Chainz ↗

Height

#208,242

Difficulty

9.905425

Transactions

Size

2.23 KB

Version

Bits

09e7c9f2

Nonce

287,436

Timestamp

10/13/2013, 9:55:51 PM

Confirmations

6,587,165

Mined by

⛏️ P2SHASHFG7yrSzLqkd9HVzwqEYamvkSLp7W6Wj

Merkle Root

bd03eb344fe5868c36acfec35e23cc44b02b3313b937c6388fcbb6422c1d2c2c

Transactions (3)

Coinbase7bc5ee0136d369…1788b7e0a73773

1 in → 1 out10.2100 XPM109 B

ASHFG7yr…SLp7W6Wj

6d2a3e103726c7…af85c9a666383b

11 in → 2 out681.4886 XPM1.67 KB

AMAeupWD…WhWyLcuK AMLr4BYJ…kmz9P84k

bfd4b9d363d99c…6fadc060d10617

2 in → 2 out13.1747 XPM375 B

Ab3dSvM7…Qoxxb9tp AJGHfZ6b…eRBvfvjR

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.

6.443 × 10⁹⁶(97-digit number)

64435741867739179993…71584112858420055039

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

6.443 × 10⁹⁶(97-digit number)

64435741867739179993…71584112858420055039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.443 × 10⁹⁶(97-digit number)

64435741867739179993…71584112858420055041

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

1.288 × 10⁹⁷(98-digit number)

12887148373547835998…43168225716840110079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.288 × 10⁹⁷(98-digit number)

12887148373547835998…43168225716840110081

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

2.577 × 10⁹⁷(98-digit number)

25774296747095671997…86336451433680220159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.577 × 10⁹⁷(98-digit number)

25774296747095671997…86336451433680220161

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

5.154 × 10⁹⁷(98-digit number)

51548593494191343995…72672902867360440319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.154 × 10⁹⁷(98-digit number)

51548593494191343995…72672902867360440321

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

1.030 × 10⁹⁸(99-digit number)

10309718698838268799…45345805734720880639

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