Block #2,376,528

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/12/2017, 4:21:20 PM · Difficulty 10.8815 · 4,467,979 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

084f90c8881c06405ea2a4db89d18a39977ad905cc43586e3166e17d55c5371e

View on Chainz ↗

Height

#2,376,528

Difficulty

10.881527

Transactions

Size

1.15 KB

Version

Bits

0ae1abbf

Nonce

481,990,849

Timestamp

11/12/2017, 4:21:20 PM

Confirmations

4,467,979

Mined by

⛏️ P2SHASjcQ8PR7zQPbYTuXaQaDRXZrFzoriigih

Merkle Root

9eef5b839ff748add2e575e8cff3b87413c475b1067b39297a1adb0d844ee6ab

Transactions (4)

Coinbasedc1115706399cf…3b81728a5921b4

1 in → 1 out8.4600 XPM109 B

ASjcQ8PR…zoriigih

69518564ded568…644af4d7aa3a41

1 in → 2 out7.3529 XPM226 B

AVWSPiZW…QXNwvdYM AZh1RNpw…PLq154yU

e0ed90f6d1e7ac…24daf0d9638495

1 in → 2 out4.3077 XPM227 B

AKatK3j1…WGrp4VZL Adapa9Yf…MQGrh5MG

719689cec9a16b…c2728cbfa27a0b

3 in → 2 out4.1491 XPM523 B

AcbV2azg…MA9XG2wk Abhdy697…AKY58YAf

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.

1.135 × 10⁹⁷(98-digit number)

11358983915053828069…47756068019721379839

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

1.135 × 10⁹⁷(98-digit number)

11358983915053828069…47756068019721379839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.135 × 10⁹⁷(98-digit number)

11358983915053828069…47756068019721379841

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

2.271 × 10⁹⁷(98-digit number)

22717967830107656139…95512136039442759679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.271 × 10⁹⁷(98-digit number)

22717967830107656139…95512136039442759681

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

4.543 × 10⁹⁷(98-digit number)

45435935660215312279…91024272078885519359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.543 × 10⁹⁷(98-digit number)

45435935660215312279…91024272078885519361

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

9.087 × 10⁹⁷(98-digit number)

90871871320430624558…82048544157771038719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.087 × 10⁹⁷(98-digit number)

90871871320430624558…82048544157771038721

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

1.817 × 10⁹⁸(99-digit number)

18174374264086124911…64097088315542077439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.817 × 10⁹⁸(99-digit number)

18174374264086124911…64097088315542077441

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 #2,376,528

Cookie Preferences