Block #215,753

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 7:30:16 AM · Difficulty 9.9255 · 6,627,244 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6551b227abf810c84b8ed62158d82fe43bea548bea717a621c36e576c958d4a9

View on Chainz ↗

Height

#215,753

Difficulty

9.925461

Transactions

Size

4.93 KB

Version

Bits

09eceb02

Nonce

39,857

Timestamp

10/18/2013, 7:30:16 AM

Confirmations

6,627,244

Mined by

⛏️ JR`JQAJkehH7gZuwmYBdfcxqvEWLveE7vAGtaHJ

Merkle Root

92487652f6535a65a58894ad3f9f8c0be835a0bf6d4f3aad9d2f695857b99825

Transactions (1)

Coinbase92487652f6535a…2f695857b99825

1 in → 144 out10.0800 XPM4.84 KB

AJkehH7g…7vAGtaHJ AQbu7mdU…kaYDc9Lq ANKaqdoT…rPahfJui AUsdND2U…PxHWEPmG AXZFLMG5…K1ffobqG

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.

3.027 × 10⁹⁴(95-digit number)

30278030905901435532…63945793137414092799

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

3.027 × 10⁹⁴(95-digit number)

30278030905901435532…63945793137414092799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.027 × 10⁹⁴(95-digit number)

30278030905901435532…63945793137414092801

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

6.055 × 10⁹⁴(95-digit number)

60556061811802871064…27891586274828185599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.055 × 10⁹⁴(95-digit number)

60556061811802871064…27891586274828185601

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

1.211 × 10⁹⁵(96-digit number)

12111212362360574212…55783172549656371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.211 × 10⁹⁵(96-digit number)

12111212362360574212…55783172549656371201

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

2.422 × 10⁹⁵(96-digit number)

24222424724721148425…11566345099312742399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.422 × 10⁹⁵(96-digit number)

24222424724721148425…11566345099312742401

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

4.844 × 10⁹⁵(96-digit number)

48444849449442296851…23132690198625484799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.844 × 10⁹⁵(96-digit number)

48444849449442296851…23132690198625484801

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 #215,753

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