Block #258,065

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/12/2013, 8:08:22 PM · Difficulty 9.9762 · 6,543,749 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

59da99c63eed4577cb3a311e4c52b3164ad97dbf3502f3a4da649bc4ad9be124

View on Chainz ↗

Height

#258,065

Difficulty

9.976200

Transactions

Size

606 B

Version

Bits

09f9e840

Nonce

6,575

Timestamp

11/12/2013, 8:08:22 PM

Confirmations

6,543,749

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

64fe176baddfd29d3caeb4294ea7607c12b351c86f6df2b544bd92456aa50154

Transactions (2)

Coinbase8ad57341f52295…0c9cfac69b5255

1 in → 2 out10.0400 XPM141 B

AdGRRh1e…QmctLb24 ASNt3cJa…L5zCqAYM

f3810a12f31936…65f9e00b2a4316

2 in → 2 out32.8440 XPM374 B

AUC766Yj…kTCsi6qy ATjLuGyA…b2LyEFzM

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.

2.278 × 10⁹⁶(97-digit number)

22784844509490633601…11416035148683752359

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

2.278 × 10⁹⁶(97-digit number)

22784844509490633601…11416035148683752359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.278 × 10⁹⁶(97-digit number)

22784844509490633601…11416035148683752361

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

4.556 × 10⁹⁶(97-digit number)

45569689018981267203…22832070297367504719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.556 × 10⁹⁶(97-digit number)

45569689018981267203…22832070297367504721

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

9.113 × 10⁹⁶(97-digit number)

91139378037962534407…45664140594735009439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.113 × 10⁹⁶(97-digit number)

91139378037962534407…45664140594735009441

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

1.822 × 10⁹⁷(98-digit number)

18227875607592506881…91328281189470018879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.822 × 10⁹⁷(98-digit number)

18227875607592506881…91328281189470018881

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

3.645 × 10⁹⁷(98-digit number)

36455751215185013762…82656562378940037759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.645 × 10⁹⁷(98-digit number)

36455751215185013762…82656562378940037761

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