Block #287,194

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 5:30:29 AM · Difficulty 9.9864 · 6,530,647 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa45d90ccb4fd50e12bcf81db88ca1c0131c88dad53a090ebec53c9cd052d512

View on Chainz ↗

Height

#287,194

Difficulty

9.986400

Transactions

Size

1.04 KB

Version

Bits

09fc84ae

Nonce

55,307

Timestamp

12/1/2013, 5:30:29 AM

Confirmations

6,530,647

Mined by

⛏️ P2SHAYaTpnoDjg4iRHnzSs6AaFf5TqEJq25nUy

Merkle Root

007a5e1e414163e4a4d2cc5ddf6c3baed15ba835510e920d1e8a371581665390

Transactions (3)

Coinbasef650ed386df6d6…e6ad7c3fdd3f31

1 in → 2 out10.0300 XPM141 B

AYaTpnoD…EJq25nUy ASNt3cJa…L5zCqAYM

00de0b611b9638…66414975e4fd0f

4 in → 2 out291.1345 XPM670 B

AZgULaL1…axWspE78 AJW6ya5q…SLry3FHT

d9082976d87a45…713867d2aefef9

1 in → 1 out10.0200 XPM157 B

AbP1iY2S…QXTtEVYb

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.

3.449 × 10¹⁰⁴(105-digit number)

34491684093349539228…83758129784355716639

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

3.449 × 10¹⁰⁴(105-digit number)

34491684093349539228…83758129784355716639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.449 × 10¹⁰⁴(105-digit number)

34491684093349539228…83758129784355716641

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

6.898 × 10¹⁰⁴(105-digit number)

68983368186699078456…67516259568711433279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.898 × 10¹⁰⁴(105-digit number)

68983368186699078456…67516259568711433281

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

1.379 × 10¹⁰⁵(106-digit number)

13796673637339815691…35032519137422866559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.379 × 10¹⁰⁵(106-digit number)

13796673637339815691…35032519137422866561

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

2.759 × 10¹⁰⁵(106-digit number)

27593347274679631382…70065038274845733119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.759 × 10¹⁰⁵(106-digit number)

27593347274679631382…70065038274845733121

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

5.518 × 10¹⁰⁵(106-digit number)

55186694549359262765…40130076549691466239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.518 × 10¹⁰⁵(106-digit number)

55186694549359262765…40130076549691466241

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 #287,194

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