Block #501,095

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/19/2014, 1:57:40 PM · Difficulty 10.8024 · 6,311,554 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3f35efea7b1e9784686dc9b115c7636fd330b39892828b02f4b74da3e42db2c8

View on Chainz ↗

Height

#501,095

Difficulty

10.802400

Transactions

Size

6.80 KB

Version

Bits

0acd6a1c

Nonce

37,355

Timestamp

4/19/2014, 1:57:40 PM

Confirmations

6,311,554

Mined by

⛏️ P2SHATZNcKao4GUjcN2DNRa65sC3ivGaeEW5DP

Merkle Root

62220630c992f1b18fa0dc2280955d82ca8b645348fb02396eb39787bf827378

Transactions (2)

Coinbaseaf4eff2ef97203…900dcbbdcd3fa7

1 in → 1 out8.6300 XPM112 B

ATZNcKao…GaeEW5DP

dc937f0b7f64c6…8dcc281bb74aa0

48 in → 2 out36880.2505 XPM6.60 KB

AFxjEsPo…dWj6rnkw AUvPKodv…yKADfbFQ

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.

1.229 × 10⁹⁶(97-digit number)

12291605562306035386…58157223756807627399

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

1.229 × 10⁹⁶(97-digit number)

12291605562306035386…58157223756807627399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.229 × 10⁹⁶(97-digit number)

12291605562306035386…58157223756807627401

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

2.458 × 10⁹⁶(97-digit number)

24583211124612070773…16314447513615254799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.458 × 10⁹⁶(97-digit number)

24583211124612070773…16314447513615254801

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

4.916 × 10⁹⁶(97-digit number)

49166422249224141546…32628895027230509599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.916 × 10⁹⁶(97-digit number)

49166422249224141546…32628895027230509601

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

9.833 × 10⁹⁶(97-digit number)

98332844498448283092…65257790054461019199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.833 × 10⁹⁶(97-digit number)

98332844498448283092…65257790054461019201

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

1.966 × 10⁹⁷(98-digit number)

19666568899689656618…30515580108922038399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.966 × 10⁹⁷(98-digit number)

19666568899689656618…30515580108922038401

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 #501,095

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