Block #475,374

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 5:01:56 AM · Difficulty 10.4554 · 6,329,715 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

db710d40d49459ea52b65c0ba0a24d0ea781f2aac28e6f0b3142761ae2412212

View on Chainz ↗

Height

#475,374

Difficulty

10.455400

Transactions

Size

936 B

Version

Bits

0a749515

Nonce

68,123

Timestamp

4/5/2014, 5:01:56 AM

Confirmations

6,329,715

Mined by

AGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

6e655b49254342c1b21a658892cf37706fe3c25a6630f9a475fc21567786ef77

Transactions (1)

Coinbase6e655b49254342…fc21567786ef77

1 in → 23 out9.1300 XPM845 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh AdoqUYAy…tJ482T9b AUFKXvnz…342ApNcm AZMKfLyJ…k2aFigjh

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.

3.924 × 10⁹⁷(98-digit number)

39247058005679484322…77386859198100874239

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

3.924 × 10⁹⁷(98-digit number)

39247058005679484322…77386859198100874239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.924 × 10⁹⁷(98-digit number)

39247058005679484322…77386859198100874241

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

7.849 × 10⁹⁷(98-digit number)

78494116011358968645…54773718396201748479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.849 × 10⁹⁷(98-digit number)

78494116011358968645…54773718396201748481

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

1.569 × 10⁹⁸(99-digit number)

15698823202271793729…09547436792403496959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.569 × 10⁹⁸(99-digit number)

15698823202271793729…09547436792403496961

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

3.139 × 10⁹⁸(99-digit number)

31397646404543587458…19094873584806993919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.139 × 10⁹⁸(99-digit number)

31397646404543587458…19094873584806993921

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

6.279 × 10⁹⁸(99-digit number)

62795292809087174916…38189747169613987839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.279 × 10⁹⁸(99-digit number)

62795292809087174916…38189747169613987841

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