Block #3,049,045

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 2/12/2019, 12:30:10 AM · Difficulty 10.9961 · 3,791,366 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

591bd8aeb6af61d2d6345a71d9aa7fb6d5566dbc7020a17665d8018333e9c56e

View on Chainz ↗

Height

#3,049,045

Difficulty

10.996080

Transactions

Size

571 B

Version

Bits

0afeff1a

Nonce

1,889,584,039

Timestamp

2/12/2019, 12:30:10 AM

Confirmations

3,791,366

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

aaddbda2ab8fbb6552150cc03200131ffb00b61ffd520df3592eb251ba656638

Transactions (2)

Coinbasec631798efbc6a2…8696478199cade

1 in → 1 out8.2700 XPM109 B

AbXwmGxD…4XXYP765

25ee3aae433d5c…ce6b43932839c8

2 in → 2 out316.5866 XPM373 B

AacF1tXW…JuBVBCCS AeTHTL7A…vT1872bk

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.

1.460 × 10⁹²(93-digit number)

14604683296627775217…80002705858692651529

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

1.460 × 10⁹²(93-digit number)

14604683296627775217…80002705858692651529

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.460 × 10⁹²(93-digit number)

14604683296627775217…80002705858692651531

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

2.920 × 10⁹²(93-digit number)

29209366593255550435…60005411717385303059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.920 × 10⁹²(93-digit number)

29209366593255550435…60005411717385303061

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

5.841 × 10⁹²(93-digit number)

58418733186511100870…20010823434770606119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.841 × 10⁹²(93-digit number)

58418733186511100870…20010823434770606121

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

1.168 × 10⁹³(94-digit number)

11683746637302220174…40021646869541212239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.168 × 10⁹³(94-digit number)

11683746637302220174…40021646869541212241

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

2.336 × 10⁹³(94-digit number)

23367493274604440348…80043293739082424479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.336 × 10⁹³(94-digit number)

23367493274604440348…80043293739082424481

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

4.673 × 10⁹³(94-digit number)

46734986549208880696…60086587478164848959

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

4.673 × 10⁹³(94-digit number)

46734986549208880696…60086587478164848961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #3,049,045

Cookie Preferences