Block #456,854

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 12:27:28 PM · Difficulty 10.4175 · 6,359,200 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3dc72d5945fef2465f8f0fb502ffc927d0ad472b95049173e02de0921aba49ff

View on Chainz ↗

Height

#456,854

Difficulty

10.417545

Transactions

Size

1.16 KB

Version

Bits

0a6ae43d

Nonce

9,748

Timestamp

3/23/2014, 12:27:28 PM

Confirmations

6,359,200

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c7ab92f1b625a2f52c7e79ac77f38e1efb3fa9fcf04865f7ef486ad2393badae

Transactions (3)

Coinbase03c43b6074da71…ff3446ff2e82a4

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

2b13875286c6d7…111acebd2c6532

4 in → 2 out1700.0800 XPM669 B

AHZzsH9j…garz17PN ANVriaZz…oT9ukRjf

a69153b6523d32…7a09259f855cc4

2 in → 2 out18.5800 XPM306 B

ALWb2mni…4AuRQrVc Abo5nRbx…qf7mMxAq

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.

1.267 × 10¹⁰⁰(101-digit number)

12672024836915627570…32920402327776322559

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

1.267 × 10¹⁰⁰(101-digit number)

12672024836915627570…32920402327776322559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.267 × 10¹⁰⁰(101-digit number)

12672024836915627570…32920402327776322561

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

2.534 × 10¹⁰⁰(101-digit number)

25344049673831255140…65840804655552645119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.534 × 10¹⁰⁰(101-digit number)

25344049673831255140…65840804655552645121

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

5.068 × 10¹⁰⁰(101-digit number)

50688099347662510280…31681609311105290239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.068 × 10¹⁰⁰(101-digit number)

50688099347662510280…31681609311105290241

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

1.013 × 10¹⁰¹(102-digit number)

10137619869532502056…63363218622210580479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.013 × 10¹⁰¹(102-digit number)

10137619869532502056…63363218622210580481

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

2.027 × 10¹⁰¹(102-digit number)

20275239739065004112…26726437244421160959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.027 × 10¹⁰¹(102-digit number)

20275239739065004112…26726437244421160961

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 #456,854

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