Block #268,834

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 11:46:46 AM · Difficulty 9.9563 · 6,522,170 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b8244e99c07d22362c683254f3aa6b6673261fdbac0e93fdd9a40f4b40d47cb9

View on Chainz ↗

Height

#268,834

Difficulty

9.956265

Transactions

Size

1.93 KB

Version

Bits

09f4cdc2

Nonce

56,504

Timestamp

11/22/2013, 11:46:46 AM

Confirmations

6,522,170

Merkle Root

f3b02f43719e9fd1e94e0172e464426305fd06a25a208704412309906298b081

Transactions (2)

Coinbase346fea642a242e…e7e313d510c4b7

1 in → 47 out10.0500 XPM1.62 KB

ARiyx2fi…3haoQexs AabHNb1B…GRoingRy ARpndEmc…Hg792kEk ANHbaxZp…XjnHCJJs AVzhvfTX…ZzNJYq61

2dc5ded66a1a0c…3ccb293b5afc2d

1 in → 3 out10.0500 XPM226 B

AVKfZvtY…sCa4NTcM AeKNrjNj…1NEq95Ta AMuPGPXT…eMMNvd8v

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.

6.279 × 10⁹⁷(98-digit number)

62794386304470656503…79272120005140280319

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

6.279 × 10⁹⁷(98-digit number)

62794386304470656503…79272120005140280319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.279 × 10⁹⁷(98-digit number)

62794386304470656503…79272120005140280321

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

1.255 × 10⁹⁸(99-digit number)

12558877260894131300…58544240010280560639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.255 × 10⁹⁸(99-digit number)

12558877260894131300…58544240010280560641

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

2.511 × 10⁹⁸(99-digit number)

25117754521788262601…17088480020561121279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.511 × 10⁹⁸(99-digit number)

25117754521788262601…17088480020561121281

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

5.023 × 10⁹⁸(99-digit number)

50235509043576525202…34176960041122242559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.023 × 10⁹⁸(99-digit number)

50235509043576525202…34176960041122242561

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

1.004 × 10⁹⁹(100-digit number)

10047101808715305040…68353920082244485119

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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