Block #22,288

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/12/2013, 4:51:07 PM · Difficulty 7.9511 · 6,770,485 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b3dc517ba0d8a044a73bdf2bcd3cf54ab4fc98eea99932e1dcdb4d09be177e7

View on Chainz ↗

Height

#22,288

Difficulty

7.951094

Transactions

Size

724 B

Version

Bits

07f37ae4

Nonce

579

Timestamp

7/12/2013, 4:51:07 PM

Confirmations

6,770,485

Merkle Root

2461e6bae447b9fe1a1f65d78e130689eb578f8c02e694b739bee6cc2603351f

Transactions (2)

Coinbase01d19fb2ede9a7…c4b32a1fa160ad

1 in → 1 out15.8100 XPM108 B

AV3Mx3Aq…AKiwER2W

9cb5bfdf7e92f5…65549ac33ee42c

3 in → 2 out81.3000 XPM524 B

AJqZPYGZ…NzEot7dv AGn6oF9g…yemnwCer

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.

8.093 × 10⁹⁹(100-digit number)

80937628682862171628…15981384208744552529

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

8.093 × 10⁹⁹(100-digit number)

80937628682862171628…15981384208744552529

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.093 × 10⁹⁹(100-digit number)

80937628682862171628…15981384208744552531

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

1.618 × 10¹⁰⁰(101-digit number)

16187525736572434325…31962768417489105059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.618 × 10¹⁰⁰(101-digit number)

16187525736572434325…31962768417489105061

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

3.237 × 10¹⁰⁰(101-digit number)

32375051473144868651…63925536834978210119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.237 × 10¹⁰⁰(101-digit number)

32375051473144868651…63925536834978210121

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

6.475 × 10¹⁰⁰(101-digit number)

64750102946289737302…27851073669956420239

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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