Block #430,255

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/5/2014, 9:26:49 AM · Difficulty 10.3412 · 6,387,720 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a9ac90010485fba92765a5c3a4721d54b76975d1ee37fe0724697fb184e54b9d

View on Chainz ↗

Height

#430,255

Difficulty

10.341201

Transactions

Size

938 B

Version

Bits

0a5758ee

Nonce

374,286

Timestamp

3/5/2014, 9:26:49 AM

Confirmations

6,387,720

Mined by

⛏️ s3AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

a2e7a8d861678d47cbcc7e017dfa8eb4c9b103611aed5791621223392b08a14a

Transactions (1)

Coinbasea2e7a8d861678d…1223392b08a14a

1 in → 23 out9.3400 XPM845 B

AdFLJFhb…bsaVkAyh AVRMvm7T…6PC6keBx AZqjMFvv…G8aw2zC8 AcuM7XiJ…5uND8Jce ATp4jJhs…TbSgR8Qb

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.

3.365 × 10¹⁰¹(102-digit number)

33654232756744420240…67547843009527383359

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

3.365 × 10¹⁰¹(102-digit number)

33654232756744420240…67547843009527383359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.365 × 10¹⁰¹(102-digit number)

33654232756744420240…67547843009527383361

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

6.730 × 10¹⁰¹(102-digit number)

67308465513488840480…35095686019054766719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.730 × 10¹⁰¹(102-digit number)

67308465513488840480…35095686019054766721

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

1.346 × 10¹⁰²(103-digit number)

13461693102697768096…70191372038109533439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.346 × 10¹⁰²(103-digit number)

13461693102697768096…70191372038109533441

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

2.692 × 10¹⁰²(103-digit number)

26923386205395536192…40382744076219066879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.692 × 10¹⁰²(103-digit number)

26923386205395536192…40382744076219066881

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

5.384 × 10¹⁰²(103-digit number)

53846772410791072384…80765488152438133759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.384 × 10¹⁰²(103-digit number)

53846772410791072384…80765488152438133761

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 #430,255

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