Block #3,482,274

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/19/2019, 8:49:23 AM · Difficulty 10.9786 · 3,359,584 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

60a475625bcbe7abbbe7b43ea2ed06f697bab639bc469ab94a4a3e6812f466bf

View on Chainz ↗

Height

#3,482,274

Difficulty

10.978551

Transactions

Size

1.35 KB

Version

Bits

0afa8255

Nonce

216,446,281

Timestamp

12/19/2019, 8:49:23 AM

Confirmations

3,359,584

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

b46517ddedc954afebe1077601509fddaeab004555502bf1813e85ce9384c025

Transactions (4)

Coinbasec2646520fcb4ab…cd26afc24b5e27

1 in → 1 out8.3100 XPM110 B

ASiq2qtK…VMhmk7yL

ddcbba54346309…f6580f1ebc551e

4 in → 2 out33.1200 XPM531 B

ASiq2qtK…VMhmk7yL AMFxoiZV…2UX5WRMn

ef01269d031a6b…ebb1c5a7bb690c

1 in → 2 out8.2700 XPM193 B

ASiq2qtK…VMhmk7yL AQEsCWzC…yBYFaZWT

36eac9649c9cc6…a9439e58b05486

3 in → 2 out23.1111 XPM455 B

ASiq2qtK…VMhmk7yL AYMtuoYy…7yNhdSiV

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.

1.884 × 10⁹⁸(99-digit number)

18840526523302772162…73650047614462853119

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

1.884 × 10⁹⁸(99-digit number)

18840526523302772162…73650047614462853119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.884 × 10⁹⁸(99-digit number)

18840526523302772162…73650047614462853121

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

3.768 × 10⁹⁸(99-digit number)

37681053046605544325…47300095228925706239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.768 × 10⁹⁸(99-digit number)

37681053046605544325…47300095228925706241

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

7.536 × 10⁹⁸(99-digit number)

75362106093211088651…94600190457851412479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.536 × 10⁹⁸(99-digit number)

75362106093211088651…94600190457851412481

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

1.507 × 10⁹⁹(100-digit number)

15072421218642217730…89200380915702824959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.507 × 10⁹⁹(100-digit number)

15072421218642217730…89200380915702824961

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

3.014 × 10⁹⁹(100-digit number)

30144842437284435460…78400761831405649919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.014 × 10⁹⁹(100-digit number)

30144842437284435460…78400761831405649921

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

6.028 × 10⁹⁹(100-digit number)

60289684874568870920…56801523662811299839

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 #3,482,274

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