Block #287,225

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 5:51:34 AM · Difficulty 9.9864 · 6,516,543 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

35a2b46408190a13c5be51e1826bba389d7d6cb4857414438f9eb0bd97f9f23d

View on Chainz ↗

Height

#287,225

Difficulty

9.986424

Transactions

Size

1.11 KB

Version

Bits

09fc8641

Nonce

9,422

Timestamp

12/1/2013, 5:51:34 AM

Confirmations

6,516,543

Mined by

⛏️ aaRAYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

c42293bc00d4e86c12e90575ff7636301b66199f5bfa214badb0020d9a6f3777

Transactions (1)

Coinbasec42293bc00d4e8…b0020d9a6f3777

1 in → 29 out9.9900 XPM1.02 KB

AYcLTeXR…bscgPops AGFAJ5YL…ZEnBbk6G AWZd1qVJ…9pj9yfPa ALaSmG93…4TA3uNAR Ad9pSzHt…cpJ3y2zz

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.

2.678 × 10⁹⁴(95-digit number)

26787382307630669060…48602494428748456959

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

2.678 × 10⁹⁴(95-digit number)

26787382307630669060…48602494428748456959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.678 × 10⁹⁴(95-digit number)

26787382307630669060…48602494428748456961

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

5.357 × 10⁹⁴(95-digit number)

53574764615261338121…97204988857496913919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.357 × 10⁹⁴(95-digit number)

53574764615261338121…97204988857496913921

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

1.071 × 10⁹⁵(96-digit number)

10714952923052267624…94409977714993827839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.071 × 10⁹⁵(96-digit number)

10714952923052267624…94409977714993827841

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

2.142 × 10⁹⁵(96-digit number)

21429905846104535248…88819955429987655679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.142 × 10⁹⁵(96-digit number)

21429905846104535248…88819955429987655681

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

4.285 × 10⁹⁵(96-digit number)

42859811692209070497…77639910859975311359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.285 × 10⁹⁵(96-digit number)

42859811692209070497…77639910859975311361

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