Block #298,551

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/7/2013, 10:07:05 AM · Difficulty 9.9919 · 6,508,289 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ed21a087d04228127a0d856f45230c5fe3e8ae76d39b8cdfb11315a20548e44

View on Chainz ↗

Height

#298,551

Difficulty

9.991938

Transactions

Size

1.18 KB

Version

Bits

09fdefa5

Nonce

8,482

Timestamp

12/7/2013, 10:07:05 AM

Confirmations

6,508,289

Mined by

⛏️ 7aR'AWxMqAjDsVDnL1kBWfXmRHrWXZjNai1Anq

Merkle Root

0a1b331517a9b517e7099b3ab4558ff5efbc7f8c14366faba1aa9cbe0908c4b0

Transactions (1)

Coinbase0a1b331517a9b5…aa9cbe0908c4b0

1 in → 31 out9.9800 XPM1.09 KB

AWxMqAjD…jNai1Anq AYDL6Wib…4YqySJHr AKwqFUdz…D4jGNKFN Acs9SHrk…QJSB8SFG AUW89vJd…BiczGLRw

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.

4.677 × 10⁹⁴(95-digit number)

46776067638645277009…16585145867570411519

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

4.677 × 10⁹⁴(95-digit number)

46776067638645277009…16585145867570411519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.677 × 10⁹⁴(95-digit number)

46776067638645277009…16585145867570411521

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

9.355 × 10⁹⁴(95-digit number)

93552135277290554018…33170291735140823039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.355 × 10⁹⁴(95-digit number)

93552135277290554018…33170291735140823041

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

1.871 × 10⁹⁵(96-digit number)

18710427055458110803…66340583470281646079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.871 × 10⁹⁵(96-digit number)

18710427055458110803…66340583470281646081

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

3.742 × 10⁹⁵(96-digit number)

37420854110916221607…32681166940563292159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.742 × 10⁹⁵(96-digit number)

37420854110916221607…32681166940563292161

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

7.484 × 10⁹⁵(96-digit number)

74841708221832443214…65362333881126584319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.484 × 10⁹⁵(96-digit number)

74841708221832443214…65362333881126584321

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 #298,551

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