Block #1,397,926

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/3/2016, 11:05:14 PM · Difficulty 10.8081 · 5,429,148 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7124e1ff0df920e6813cdaaf36b37efb01bec94b26ae750eb59050313592626b

View on Chainz ↗

Height

#1,397,926

Difficulty

10.808109

Transactions

Size

3.89 KB

Version

Bits

0acee034

Nonce

178,349,963

Timestamp

1/3/2016, 11:05:14 PM

Confirmations

5,429,148

Mined by

⛏️ P2SHAFu8ZtDyybznYFa7ZWC2bB46N1S8Zb8KSZ

Merkle Root

14ab10e455ad81db1650602dd0d407bc67101457b3d107555354658772d67993

Transactions (3)

Coinbase7161d4431bb60c…1b8d650cda4b61

1 in → 1 out8.5900 XPM110 B

AFu8ZtDy…S8Zb8KSZ

54d29fc080e0ef…3b6cb7218068ec

1 in → 51 out8.1965 XPM1.85 KB

AeR7Gabv…Bg1SL7Sd AeTKexgt…VW979T6T AaPNaTmu…rC1ndNgP AMznJws3…LpVbLJfo AekjCLh2…RqH7bwU9

de47a60645aac9…b92f3b2ea74da0

1 in → 51 out2.3815 XPM1.85 KB

AeNLLj9X…DfYPyRWx AJ6UN5H6…goz53SCr AYgQVzur…HfLqzYWT AamAUsyL…j7LXkSDA AZ2Dv6vs…YoKVyFme

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.

8.264 × 10⁹⁵(96-digit number)

82645273553613690915…83616727467676840959

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

8.264 × 10⁹⁵(96-digit number)

82645273553613690915…83616727467676840959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.264 × 10⁹⁵(96-digit number)

82645273553613690915…83616727467676840961

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

1.652 × 10⁹⁶(97-digit number)

16529054710722738183…67233454935353681919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.652 × 10⁹⁶(97-digit number)

16529054710722738183…67233454935353681921

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

3.305 × 10⁹⁶(97-digit number)

33058109421445476366…34466909870707363839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.305 × 10⁹⁶(97-digit number)

33058109421445476366…34466909870707363841

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

6.611 × 10⁹⁶(97-digit number)

66116218842890952732…68933819741414727679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.611 × 10⁹⁶(97-digit number)

66116218842890952732…68933819741414727681

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

1.322 × 10⁹⁷(98-digit number)

13223243768578190546…37867639482829455359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.322 × 10⁹⁷(98-digit number)

13223243768578190546…37867639482829455361

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 #1,397,926

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