Block #217,987

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/19/2013, 4:20:18 PM · Difficulty 9.9294 · 6,591,651 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

11132b0f383344577689cfa98eba87556e3173bbcaa96d7c60979033a04bd6d0

View on Chainz ↗

Height

#217,987

Difficulty

9.929430

Transactions

Size

1.45 KB

Version

Bits

09edef1e

Nonce

328,248

Timestamp

10/19/2013, 4:20:18 PM

Confirmations

6,591,651

Mined by

⛏️ SRbZARpndEmcGyFUFhdFVbgqJiPBAmHg792kEk

Merkle Root

492c6162b847173e52dc7652f3bb1eb8a39f59d12a87cb7ee54b51d26abf086c

Transactions (2)

Coinbasec9c14240c5dce5…0033a2540f4aef

1 in → 15 out10.1300 XPM572 B

ARpndEmc…Hg792kEk AeBk6YnL…JRXHDtz8 AbeUZSvK…ijGzuyjz AKXeSXzu…yeuNjvhB AN4upMPL…NCifBT7h

40cac4aa7fcef5…0e3daa16680445

5 in → 2 out85.9099 XPM820 B

AMwDgG5B…gCPWNEyP AQvftpUz…fw8JQAtz

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.

1.332 × 10⁹⁷(98-digit number)

13322371814385045580…66350961647277496319

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

1.332 × 10⁹⁷(98-digit number)

13322371814385045580…66350961647277496319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.332 × 10⁹⁷(98-digit number)

13322371814385045580…66350961647277496321

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

2.664 × 10⁹⁷(98-digit number)

26644743628770091161…32701923294554992639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.664 × 10⁹⁷(98-digit number)

26644743628770091161…32701923294554992641

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

5.328 × 10⁹⁷(98-digit number)

53289487257540182323…65403846589109985279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.328 × 10⁹⁷(98-digit number)

53289487257540182323…65403846589109985281

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

1.065 × 10⁹⁸(99-digit number)

10657897451508036464…30807693178219970559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.065 × 10⁹⁸(99-digit number)

10657897451508036464…30807693178219970561

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

2.131 × 10⁹⁸(99-digit number)

21315794903016072929…61615386356439941119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.131 × 10⁹⁸(99-digit number)

21315794903016072929…61615386356439941121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #217,987

Cookie Preferences