Block #475,024

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 11:10:41 PM · Difficulty 10.4556 · 6,330,832 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f720abbb7966032fd92a36489613d58add34c474ccc6d58dda26c25e002094ef

View on Chainz ↗

Height

#475,024

Difficulty

10.455627

Transactions

Size

1.40 KB

Version

Bits

0a74a3fb

Nonce

112,352

Timestamp

4/4/2014, 11:10:41 PM

Confirmations

6,330,832

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

7ec177fca3de18b9815541925cdcfc9a5fca3fc83d8f86073b399d276d43637b

Transactions (3)

Coinbasece0b633aadceaa…2330b91da07f13

1 in → 23 out9.1500 XPM845 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH APtc8nU2…tp6qFHwW AUzEPJFG…kYkA5U9V

65385c8473287b…98392f9930c163

2 in → 2 out18.4100 XPM306 B

AcSwHGsA…y9qVb1K4 ATx8iQ8h…XbxyuQRB

3e2610dc7fc95e…c4a83188811fe3

1 in → 1 out0.3584 XPM192 B

AGXFqSyj…FxquNuxH

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.

4.720 × 10⁹⁹(100-digit number)

47208221747680733161…35715160908540241279

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

4.720 × 10⁹⁹(100-digit number)

47208221747680733161…35715160908540241279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.720 × 10⁹⁹(100-digit number)

47208221747680733161…35715160908540241281

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

9.441 × 10⁹⁹(100-digit number)

94416443495361466323…71430321817080482559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.441 × 10⁹⁹(100-digit number)

94416443495361466323…71430321817080482561

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

1.888 × 10¹⁰⁰(101-digit number)

18883288699072293264…42860643634160965119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.888 × 10¹⁰⁰(101-digit number)

18883288699072293264…42860643634160965121

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

3.776 × 10¹⁰⁰(101-digit number)

37766577398144586529…85721287268321930239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.776 × 10¹⁰⁰(101-digit number)

37766577398144586529…85721287268321930241

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

7.553 × 10¹⁰⁰(101-digit number)

75533154796289173058…71442574536643860479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.553 × 10¹⁰⁰(101-digit number)

75533154796289173058…71442574536643860481

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