Block #1,845,465

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/12/2016, 10:24:01 AM · Difficulty 10.6123 · 4,999,558 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0224e055bd782a45d37a6b9da81cac6e4128ee253c705de2780b0269819d5082

View on Chainz ↗

Height

#1,845,465

Difficulty

10.612295

Transactions

Size

6.88 KB

Version

Bits

0a9cbf63

Nonce

484,571,800

Timestamp

11/12/2016, 10:24:01 AM

Confirmations

4,999,558

Mined by

⛏️ P2SHAb3ameCqxB3nxdoYtcgE65cdExNJGWYFSF

Merkle Root

a139e0d98ed5305ffabb475988086440d2551bca460ec3f7002ee2982be2f3dd

Transactions (2)

Coinbase28feeea8cbd3e8…81a2f07de19677

1 in → 1 out8.9400 XPM110 B

Ab3ameCq…NJGWYFSF

6773ba1bc2cd93…d1a5d332cd789e

46 in → 1 out259.9300 XPM6.69 KB

AVtWEnxx…nytVBavj

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.

3.113 × 10⁹⁴(95-digit number)

31138844775900654311…52649944764372780879

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

3.113 × 10⁹⁴(95-digit number)

31138844775900654311…52649944764372780879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.113 × 10⁹⁴(95-digit number)

31138844775900654311…52649944764372780881

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

6.227 × 10⁹⁴(95-digit number)

62277689551801308622…05299889528745561759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.227 × 10⁹⁴(95-digit number)

62277689551801308622…05299889528745561761

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

1.245 × 10⁹⁵(96-digit number)

12455537910360261724…10599779057491123519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.245 × 10⁹⁵(96-digit number)

12455537910360261724…10599779057491123521

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

2.491 × 10⁹⁵(96-digit number)

24911075820720523449…21199558114982247039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.491 × 10⁹⁵(96-digit number)

24911075820720523449…21199558114982247041

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

4.982 × 10⁹⁵(96-digit number)

49822151641441046898…42399116229964494079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.982 × 10⁹⁵(96-digit number)

49822151641441046898…42399116229964494081

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 #1,845,465

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