Block #216,048

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 12:36:23 PM · Difficulty 9.9254 · 6,588,750 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6145b9ff58263083e6bfeddb1a39ecb90b0291ae53ca42096d976d11c6f01057

View on Chainz ↗

Height

#216,048

Difficulty

9.925361

Transactions

Size

1.07 KB

Version

Bits

09ece46e

Nonce

80,450

Timestamp

10/18/2013, 12:36:23 PM

Confirmations

6,588,750

Mined by

⛏️ P2SHAWoZBbYQnbHw6UTTKfy8xQtEBxrzeKgAqA

Merkle Root

91b4aeb9521e0f6d00a51a6a49684395c7797a1bc04d618f8f6a5af42ec8f4aa

Transactions (3)

Coinbase95968209a76ef1…0684b63ad20d20

1 in → 1 out10.1600 XPM109 B

AWoZBbYQ…rzeKgAqA

a9077a6f8cd4d3…ed07a47392e3bb

3 in → 2 out211.5227 XPM522 B

AJM6aWAG…whFENXCA AGcvNgL8…wmiSAm93

9ac5b3aa4cfea3…8d0072640c1e0f

2 in → 2 out10.2912 XPM375 B

ASuoUi24…FwBoFbxd AbkG2vsN…jdGLppz9

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.

3.124 × 10⁹⁸(99-digit number)

31245776089226008960…01135599457816511999

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

3.124 × 10⁹⁸(99-digit number)

31245776089226008960…01135599457816511999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.124 × 10⁹⁸(99-digit number)

31245776089226008960…01135599457816512001

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

6.249 × 10⁹⁸(99-digit number)

62491552178452017921…02271198915633023999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.249 × 10⁹⁸(99-digit number)

62491552178452017921…02271198915633024001

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

1.249 × 10⁹⁹(100-digit number)

12498310435690403584…04542397831266047999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.249 × 10⁹⁹(100-digit number)

12498310435690403584…04542397831266048001

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

2.499 × 10⁹⁹(100-digit number)

24996620871380807168…09084795662532095999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.499 × 10⁹⁹(100-digit number)

24996620871380807168…09084795662532096001

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

4.999 × 10⁹⁹(100-digit number)

49993241742761614337…18169591325064191999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.999 × 10⁹⁹(100-digit number)

49993241742761614337…18169591325064192001

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