Block #268,916

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 1:46:25 PM · Difficulty 9.9559 · 6,526,141 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

24c461c9702573cb2e458dbe4bfbbb65fc5d934285b37ec50621e46df191b70d

View on Chainz ↗

Height

#268,916

Difficulty

9.955940

Transactions

Size

425 B

Version

Bits

09f4b875

Nonce

355,851

Timestamp

11/22/2013, 1:46:25 PM

Confirmations

6,526,141

Mined by

⛏️ P2SHASUtGRx8bDVJURUf8WLJkL5tX6vh2tTKJs

Merkle Root

15653911aeae4f1309fbc2504c2101cec954a2ea9daec79c83bf96ac2a289aa8

Transactions (2)

Coinbase66efa1af81cba5…3c7b104844648b

1 in → 1 out10.0800 XPM109 B

ASUtGRx8…vh2tTKJs

6e9f67b61b7423…38090b34f1b222

1 in → 2 out161.7143 XPM225 B

AYVtfkkE…TyEM1H7C AHHxkvzD…tEYabgTc

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.

6.512 × 10⁹⁷(98-digit number)

65124083921596976952…89798472089326627199

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

6.512 × 10⁹⁷(98-digit number)

65124083921596976952…89798472089326627199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.512 × 10⁹⁷(98-digit number)

65124083921596976952…89798472089326627201

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

1.302 × 10⁹⁸(99-digit number)

13024816784319395390…79596944178653254399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.302 × 10⁹⁸(99-digit number)

13024816784319395390…79596944178653254401

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

2.604 × 10⁹⁸(99-digit number)

26049633568638790780…59193888357306508799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.604 × 10⁹⁸(99-digit number)

26049633568638790780…59193888357306508801

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

5.209 × 10⁹⁸(99-digit number)

52099267137277581561…18387776714613017599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.209 × 10⁹⁸(99-digit number)

52099267137277581561…18387776714613017601

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

1.041 × 10⁹⁹(100-digit number)

10419853427455516312…36775553429226035199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.041 × 10⁹⁹(100-digit number)

10419853427455516312…36775553429226035201

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