Block #459,372

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/25/2014, 6:50:57 AM · Difficulty 10.4157 · 6,367,383 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f1966462592d45883e306d349ede7157053be53c3c9cba40e4a5e85eb0f59e66

View on Chainz ↗

Height

#459,372

Difficulty

10.415686

Transactions

Size

1001 B

Version

Bits

0a6a6a5e

Nonce

91,199

Timestamp

3/25/2014, 6:50:57 AM

Confirmations

6,367,383

Mined by

⛏️ laS1'-uAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

271b2481332d3fb7b8c4b79413d3cc11091903d2589bb65afd8a454b09b91020

Transactions (1)

Coinbase271b2481332d3f…8a454b09b91020

1 in → 25 out9.2000 XPM913 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AQ8QAT3J…rCFKuVbR AJtNW28X…Syb4Ph5j

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.

4.961 × 10⁹⁰(91-digit number)

49612343354648729250…28297665296240305199

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

4.961 × 10⁹⁰(91-digit number)

49612343354648729250…28297665296240305199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.961 × 10⁹⁰(91-digit number)

49612343354648729250…28297665296240305201

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

9.922 × 10⁹⁰(91-digit number)

99224686709297458500…56595330592480610399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.922 × 10⁹⁰(91-digit number)

99224686709297458500…56595330592480610401

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

1.984 × 10⁹¹(92-digit number)

19844937341859491700…13190661184961220799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.984 × 10⁹¹(92-digit number)

19844937341859491700…13190661184961220801

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

3.968 × 10⁹¹(92-digit number)

39689874683718983400…26381322369922441599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.968 × 10⁹¹(92-digit number)

39689874683718983400…26381322369922441601

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

7.937 × 10⁹¹(92-digit number)

79379749367437966800…52762644739844883199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.937 × 10⁹¹(92-digit number)

79379749367437966800…52762644739844883201

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 #459,372

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