Block #284,233

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 1:35:46 AM · Difficulty 9.9823 · 6,532,866 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e88c96e1aa149ac1406be22b3576bcbb7c969b948cdcfb5d5441b0460757230

View on Chainz ↗

Height

#284,233

Difficulty

9.982334

Transactions

Size

1.58 KB

Version

Bits

09fb7a45

Nonce

4,340

Timestamp

11/30/2013, 1:35:46 AM

Confirmations

6,532,866

Mined by

⛏️ P2SHAYaTpnoDjg4iRHnzSs6AaFf5TqEJq25nUy

Merkle Root

ee99ea74c648fe01c39575f3dc2e094c43213c08e8bfa055b3e3dcd96fa59d5e

Transactions (3)

Coinbase25e2b7e290d191…b0b779916a47f2

1 in → 2 out10.0500 XPM139 B

AYaTpnoD…EJq25nUy Abiw8n3q…ZnZfgvQW

3006bc116131da…2ceb1e7be80562

6 in → 12 out42.5272 XPM1.14 KB

APkXLmsc…UtrodHyJ AMUH1Z1t…Q1XW99zU AMsrZhpd…pYrYdaoi ANXFTTtZ…bQJ6QhQc Ab1rvHLy…8AwCgFdt

0b94164524f63a…bf2a74137ee4e0

1 in → 2 out0.2970 XPM225 B

AY69m4QT…o5NoPSBG AN5b4VSx…k25CudKe

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.

1.084 × 10¹⁰⁰(101-digit number)

10845058107228559492…01214134111857433999

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

1.084 × 10¹⁰⁰(101-digit number)

10845058107228559492…01214134111857433999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.084 × 10¹⁰⁰(101-digit number)

10845058107228559492…01214134111857434001

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

2.169 × 10¹⁰⁰(101-digit number)

21690116214457118985…02428268223714867999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.169 × 10¹⁰⁰(101-digit number)

21690116214457118985…02428268223714868001

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

4.338 × 10¹⁰⁰(101-digit number)

43380232428914237970…04856536447429735999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.338 × 10¹⁰⁰(101-digit number)

43380232428914237970…04856536447429736001

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

8.676 × 10¹⁰⁰(101-digit number)

86760464857828475941…09713072894859471999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.676 × 10¹⁰⁰(101-digit number)

86760464857828475941…09713072894859472001

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

1.735 × 10¹⁰¹(102-digit number)

17352092971565695188…19426145789718943999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.735 × 10¹⁰¹(102-digit number)

17352092971565695188…19426145789718944001

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 #284,233

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