Block #427,245

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2014, 6:10:17 AM · Difficulty 10.3473 · 6,387,621 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70aea75aa0c7caf52c2a51fc2951d7165b694aaa2c9e57b643eac3014fe124eb

View on Chainz ↗

Height

#427,245

Difficulty

10.347338

Transactions

Size

901 B

Version

Bits

0a58eb2c

Nonce

658,611

Timestamp

3/3/2014, 6:10:17 AM

Confirmations

6,387,621

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

446ac7d8c6e117b4418de93ac17ffb6f27dfe3aef07b7d97e97d2cda1ca073d4

Transactions (1)

Coinbase446ac7d8c6e117…7d2cda1ca073d4

1 in → 22 out9.3300 XPM811 B

AdFLJFhb…bsaVkAyh AcuM7XiJ…5uND8Jce AZqjMFvv…G8aw2zC8 AVRMvm7T…6PC6keBx AcgDwGo8…BBFwbjVo

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.

8.852 × 10⁹⁵(96-digit number)

88526049552813332233…21034682696141852799

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

8.852 × 10⁹⁵(96-digit number)

88526049552813332233…21034682696141852799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.852 × 10⁹⁵(96-digit number)

88526049552813332233…21034682696141852801

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

1.770 × 10⁹⁶(97-digit number)

17705209910562666446…42069365392283705599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.770 × 10⁹⁶(97-digit number)

17705209910562666446…42069365392283705601

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

3.541 × 10⁹⁶(97-digit number)

35410419821125332893…84138730784567411199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.541 × 10⁹⁶(97-digit number)

35410419821125332893…84138730784567411201

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

7.082 × 10⁹⁶(97-digit number)

70820839642250665786…68277461569134822399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.082 × 10⁹⁶(97-digit number)

70820839642250665786…68277461569134822401

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

1.416 × 10⁹⁷(98-digit number)

14164167928450133157…36554923138269644799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.416 × 10⁹⁷(98-digit number)

14164167928450133157…36554923138269644801

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 #427,245

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