Block #456,517

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 7:06:19 AM · Difficulty 10.4154 · 6,369,746 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2746e8951b651ee1f446c23f4109670f695c4cd8d17110afa6badbffa8f9cf37

View on Chainz ↗

Height

#456,517

Difficulty

10.415388

Transactions

Size

777 B

Version

Bits

0a6a56d8

Nonce

666

Timestamp

3/23/2014, 7:06:19 AM

Confirmations

6,369,746

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

cdbef2f882cf2dddcc0e65e59914f5a6752cea330bd6699b49bfb7d61af6bd91

Transactions (3)

Coinbase6d2285888a175b…f1118daeed74cc

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

eb5d2f5988352a…3506f571099498

2 in → 1 out6.1064 XPM341 B

AbcrwrF1…WVksxCP6

23731759db7c50…f5af0578be88df

1 in → 2 out3.0996 XPM226 B

Ae9y1GzW…QGKLBKKw Ab5S9t3F…MLFsGv7a

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.

1.310 × 10¹⁰³(104-digit number)

13101800332291062085…08552006897112186879

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

1.310 × 10¹⁰³(104-digit number)

13101800332291062085…08552006897112186879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.310 × 10¹⁰³(104-digit number)

13101800332291062085…08552006897112186881

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

2.620 × 10¹⁰³(104-digit number)

26203600664582124171…17104013794224373759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.620 × 10¹⁰³(104-digit number)

26203600664582124171…17104013794224373761

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

5.240 × 10¹⁰³(104-digit number)

52407201329164248342…34208027588448747519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.240 × 10¹⁰³(104-digit number)

52407201329164248342…34208027588448747521

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

1.048 × 10¹⁰⁴(105-digit number)

10481440265832849668…68416055176897495039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.048 × 10¹⁰⁴(105-digit number)

10481440265832849668…68416055176897495041

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

2.096 × 10¹⁰⁴(105-digit number)

20962880531665699337…36832110353794990079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.096 × 10¹⁰⁴(105-digit number)

20962880531665699337…36832110353794990081

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 #456,517

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