Block #521,072

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/2/2014, 6:18:13 AM · Difficulty 10.8606 · 6,280,264 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b3c86c046a70daa3485ef3c9d412f8bdcf70771658e63e541b04207ca63f1553

View on Chainz ↗

Height

#521,072

Difficulty

10.860619

Transactions

Size

201 B

Version

Bits

0adc518f

Nonce

28,654

Timestamp

5/2/2014, 6:18:13 AM

Confirmations

6,280,264

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e56d0c6e9b69dc8594ca2504857f8fb1fb04e353ecc06bb074d5d6c921d92573

Transactions (1)

Coinbasee56d0c6e9b69dc…d5d6c921d92573

1 in → 1 out8.4600 XPM110 B

AeKNrjNj…1NEq95Ta

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.

3.962 × 10⁹⁷(98-digit number)

39629173671113924947…78211491626349780399

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

3.962 × 10⁹⁷(98-digit number)

39629173671113924947…78211491626349780399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.962 × 10⁹⁷(98-digit number)

39629173671113924947…78211491626349780401

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

7.925 × 10⁹⁷(98-digit number)

79258347342227849894…56422983252699560799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.925 × 10⁹⁷(98-digit number)

79258347342227849894…56422983252699560801

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

1.585 × 10⁹⁸(99-digit number)

15851669468445569978…12845966505399121599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.585 × 10⁹⁸(99-digit number)

15851669468445569978…12845966505399121601

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

3.170 × 10⁹⁸(99-digit number)

31703338936891139957…25691933010798243199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.170 × 10⁹⁸(99-digit number)

31703338936891139957…25691933010798243201

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

6.340 × 10⁹⁸(99-digit number)

63406677873782279915…51383866021596486399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.340 × 10⁹⁸(99-digit number)

63406677873782279915…51383866021596486401

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