Block #292,721

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 9:51:26 PM · Difficulty 9.9904 · 6,514,597 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a2aa1604e7ccb6d499c633bc1062c5217ea70e6c8c07b2f54743c0527af08786

View on Chainz ↗

Height

#292,721

Difficulty

9.990387

Transactions

Size

1.15 KB

Version

Bits

09fd89f9

Nonce

609,706

Timestamp

12/3/2013, 9:51:26 PM

Confirmations

6,514,597

Mined by

⛏️ qwaRQTAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

aa826535cea0edb4ae6e6c680968770c101be888eb411ea75701badd8d1f14cd

Transactions (1)

Coinbaseaa826535cea0ed…01badd8d1f14cd

1 in → 30 out9.9800 XPM1.06 KB

AZninDSu…FvgDMwC4 Ad9pSzHt…cpJ3y2zz AYcLTeXR…bscgPops AQwRN8bE…V8PsTcY9 AKde1i4d…88R1bw6g

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.

2.235 × 10⁹⁹(100-digit number)

22353418949976463263…07358929022430177279

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

2.235 × 10⁹⁹(100-digit number)

22353418949976463263…07358929022430177279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.235 × 10⁹⁹(100-digit number)

22353418949976463263…07358929022430177281

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

4.470 × 10⁹⁹(100-digit number)

44706837899952926526…14717858044860354559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.470 × 10⁹⁹(100-digit number)

44706837899952926526…14717858044860354561

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

8.941 × 10⁹⁹(100-digit number)

89413675799905853052…29435716089720709119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.941 × 10⁹⁹(100-digit number)

89413675799905853052…29435716089720709121

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

1.788 × 10¹⁰⁰(101-digit number)

17882735159981170610…58871432179441418239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.788 × 10¹⁰⁰(101-digit number)

17882735159981170610…58871432179441418241

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

3.576 × 10¹⁰⁰(101-digit number)

35765470319962341220…17742864358882836479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.576 × 10¹⁰⁰(101-digit number)

35765470319962341220…17742864358882836481

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

Block #292,721

Cookie Preferences