Block #525,949

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/5/2014, 1:42:25 AM · Difficulty 10.8820 · 6,277,757 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a8800aad0cb4c36b605a734b2c15551c7c1c373d0a9029e5d7a34d09f91c32b8

View on Chainz ↗

Height

#525,949

Difficulty

10.882018

Transactions

Size

800 B

Version

Bits

0ae1cbe8

Nonce

8,642

Timestamp

5/5/2014, 1:42:25 AM

Confirmations

6,277,757

Mined by

⛏️ }aSfAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

962e6455cc53a45452a7ddb5156d098adb1617f1a8fe82edf26d00b3c0e4fbb2

Transactions (1)

Coinbase962e6455cc53a4…6d00b3c0e4fbb2

1 in → 19 out8.4300 XPM709 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe AUbecsVa…i8zo8qRf ATKK7iFz…wZm46KN1

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.

4.323 × 10⁹⁷(98-digit number)

43238908461339145730…54508811907398297599

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

4.323 × 10⁹⁷(98-digit number)

43238908461339145730…54508811907398297599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.323 × 10⁹⁷(98-digit number)

43238908461339145730…54508811907398297601

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

8.647 × 10⁹⁷(98-digit number)

86477816922678291461…09017623814796595199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.647 × 10⁹⁷(98-digit number)

86477816922678291461…09017623814796595201

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

1.729 × 10⁹⁸(99-digit number)

17295563384535658292…18035247629593190399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.729 × 10⁹⁸(99-digit number)

17295563384535658292…18035247629593190401

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

3.459 × 10⁹⁸(99-digit number)

34591126769071316584…36070495259186380799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.459 × 10⁹⁸(99-digit number)

34591126769071316584…36070495259186380801

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

6.918 × 10⁹⁸(99-digit number)

69182253538142633168…72140990518372761599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.918 × 10⁹⁸(99-digit number)

69182253538142633168…72140990518372761601

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