Block #467,026

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/30/2014, 12:39:02 PM · Difficulty 10.4324 · 6,340,586 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

03cfbd77c9cd3c1e3bf5a9d7fd63d69254e5363e7fdd24042111597657bb845d

View on Chainz ↗

Height

#467,026

Difficulty

10.432426

Transactions

Size

2.76 KB

Version

Bits

0a6eb37e

Nonce

93,410

Timestamp

3/30/2014, 12:39:02 PM

Confirmations

6,340,586

Mined by

⛏️ RAMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

58e3c28124a00b1a265c005dd56881858a751ac2ab51de677db433107369cd64

Transactions (4)

Coinbase0fbebb1f1feeac…85ec6360c0ae8d

1 in → 3 out9.2211 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

55207f2f877383…57f908c4458287

14 in → 1 out40.1700 XPM2.06 KB

AQm4yuyC…5LjdLYx7

ee97032fd2d4cc…a73c5bc09c2e5a

1 in → 2 out19.2044 XPM227 B

AeFuFfxa…P3wJcBoU AJJUKjdn…YZpejTdt

ec59c6eabe13e5…2855107327b8b5

1 in → 2 out9.4779 XPM226 B

AZ6RRPT8…QpPnu8A2 AMVdVQUw…p7mz5iPY

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.

9.857 × 10¹⁰⁰(101-digit number)

98577099527657690401…80689664360248226159

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

9.857 × 10¹⁰⁰(101-digit number)

98577099527657690401…80689664360248226159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.857 × 10¹⁰⁰(101-digit number)

98577099527657690401…80689664360248226161

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

1.971 × 10¹⁰¹(102-digit number)

19715419905531538080…61379328720496452319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.971 × 10¹⁰¹(102-digit number)

19715419905531538080…61379328720496452321

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

3.943 × 10¹⁰¹(102-digit number)

39430839811063076160…22758657440992904639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.943 × 10¹⁰¹(102-digit number)

39430839811063076160…22758657440992904641

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

7.886 × 10¹⁰¹(102-digit number)

78861679622126152321…45517314881985809279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.886 × 10¹⁰¹(102-digit number)

78861679622126152321…45517314881985809281

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

1.577 × 10¹⁰²(103-digit number)

15772335924425230464…91034629763971618559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.577 × 10¹⁰²(103-digit number)

15772335924425230464…91034629763971618561

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 #467,026

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