Block #456,649

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 9:05:34 AM · Difficulty 10.4172 · 6,351,200 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c58555cd174a2fb7190f8fa6987426a0c8406a33d13d5e298ca26111b3650880

View on Chainz ↗

Height

#456,649

Difficulty

10.417236

Transactions

Size

1.01 KB

Version

Bits

0a6acffb

Nonce

32,968

Timestamp

3/23/2014, 9:05:34 AM

Confirmations

6,351,200

Mined by

⛏️ aS.AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d7d41b01b7489981a8f55ebc25ca11bda51dbfb2b7a9fa069f1da2f571c370d1

Transactions (1)

Coinbased7d41b01b74899…1da2f571c370d1

1 in → 26 out9.2000 XPM947 B

AQvZBsUo…hppgRZTJ AFutDVqJ…TJTJj6UF ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q AQ8QAT3J…rCFKuVbR

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.

1.018 × 10¹⁰⁰(101-digit number)

10183766333437102708…51426828468567470079

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

1.018 × 10¹⁰⁰(101-digit number)

10183766333437102708…51426828468567470079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.018 × 10¹⁰⁰(101-digit number)

10183766333437102708…51426828468567470081

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

2.036 × 10¹⁰⁰(101-digit number)

20367532666874205417…02853656937134940159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.036 × 10¹⁰⁰(101-digit number)

20367532666874205417…02853656937134940161

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

4.073 × 10¹⁰⁰(101-digit number)

40735065333748410834…05707313874269880319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.073 × 10¹⁰⁰(101-digit number)

40735065333748410834…05707313874269880321

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

8.147 × 10¹⁰⁰(101-digit number)

81470130667496821669…11414627748539760639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.147 × 10¹⁰⁰(101-digit number)

81470130667496821669…11414627748539760641

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

1.629 × 10¹⁰¹(102-digit number)

16294026133499364333…22829255497079521279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.629 × 10¹⁰¹(102-digit number)

16294026133499364333…22829255497079521281

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 #456,649

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