Block #2,944,165

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/29/2018, 7:26:14 AM · Difficulty 11.3976 · 3,889,677 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6988a56d0b5606d82f937b2c35edf4f3ecaef3ed501d2ebf4b1d607fe62e1285

View on Chainz ↗

Height

#2,944,165

Difficulty

11.397575

Transactions

Size

1.14 KB

Version

Bits

0b65c77c

Nonce

114,701,720

Timestamp

11/29/2018, 7:26:14 AM

Confirmations

3,889,677

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

20be9756814055a078bb6a0ddbf941ad636b68e387a59e4008e0bd6944e6fee3

Transactions (2)

Coinbasedace349c4f72c5…405b76c61e0def

1 in → 1 out7.7200 XPM110 B

AbXwmGxD…4XXYP765

b9fcce977261f7…3b2b388ce72228

6 in → 2 out4388.5443 XPM964 B

ARywRRZa…HVd3P31R AJ9SeYxY…z4mzQNGk

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.

2.922 × 10⁹⁸(99-digit number)

29229195706917321780…03691747202739732479

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

2.922 × 10⁹⁸(99-digit number)

29229195706917321780…03691747202739732479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.922 × 10⁹⁸(99-digit number)

29229195706917321780…03691747202739732481

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

5.845 × 10⁹⁸(99-digit number)

58458391413834643560…07383494405479464959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.845 × 10⁹⁸(99-digit number)

58458391413834643560…07383494405479464961

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

1.169 × 10⁹⁹(100-digit number)

11691678282766928712…14766988810958929919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.169 × 10⁹⁹(100-digit number)

11691678282766928712…14766988810958929921

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

2.338 × 10⁹⁹(100-digit number)

23383356565533857424…29533977621917859839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.338 × 10⁹⁹(100-digit number)

23383356565533857424…29533977621917859841

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

4.676 × 10⁹⁹(100-digit number)

46766713131067714848…59067955243835719679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.676 × 10⁹⁹(100-digit number)

46766713131067714848…59067955243835719681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

9.353 × 10⁹⁹(100-digit number)

93533426262135429696…18135910487671439359

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,944,165

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