Block #357,430

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/13/2014, 10:07:06 AM · Difficulty 10.3834 · 6,448,745 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ac5fbc34ab3bbce8698fe6ea8e5053162322630044b5619dfd4aaf9aaedf8159

View on Chainz ↗

Height

#357,430

Difficulty

10.383351

Transactions

Size

1.08 KB

Version

Bits

0a622350

Nonce

9,385

Timestamp

1/13/2014, 10:07:06 AM

Confirmations

6,448,745

Mined by

⛏️ 6taRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

2d292e0307ac1024711f1f3faa0671cf04ead01cbbce08016bccb9fdfc922e7c

Transactions (1)

Coinbase2d292e0307ac10…ccb9fdfc922e7c

1 in → 28 out9.2400 XPM1015 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AQ8QAT3J…rCFKuVbR AYckRkCF…TgDe5VSp

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.

4.017 × 10¹⁰⁷(108-digit number)

40170464266074481476…03640977596515673599

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

4.017 × 10¹⁰⁷(108-digit number)

40170464266074481476…03640977596515673599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.017 × 10¹⁰⁷(108-digit number)

40170464266074481476…03640977596515673601

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

8.034 × 10¹⁰⁷(108-digit number)

80340928532148962952…07281955193031347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.034 × 10¹⁰⁷(108-digit number)

80340928532148962952…07281955193031347201

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

1.606 × 10¹⁰⁸(109-digit number)

16068185706429792590…14563910386062694399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.606 × 10¹⁰⁸(109-digit number)

16068185706429792590…14563910386062694401

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

3.213 × 10¹⁰⁸(109-digit number)

32136371412859585180…29127820772125388799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.213 × 10¹⁰⁸(109-digit number)

32136371412859585180…29127820772125388801

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

6.427 × 10¹⁰⁸(109-digit number)

64272742825719170361…58255641544250777599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.427 × 10¹⁰⁸(109-digit number)

64272742825719170361…58255641544250777601

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