Block #3,099,034

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/18/2019, 4:51:20 PM · Difficulty 11.1095 · 3,743,825 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e1d35dc32d065623f00c2a002e3bd9cd9c4403d3e1437116592fb6afac785fa4

View on Chainz ↗

Height

#3,099,034

Difficulty

11.109515

Transactions

Size

3.16 KB

Version

Bits

0b1c0927

Nonce

1,218,850,216

Timestamp

3/18/2019, 4:51:20 PM

Confirmations

3,743,825

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

f8df444307c07a70ec58f3d9b8dadfe4550bb64dbd32616ec2f8c8aeb3ddda09

Transactions (2)

Coinbaseb2246a647374a7…af8094495f5bfe

1 in → 1 out8.1300 XPM110 B

AbXwmGxD…4XXYP765

28d1183fd8cd13…7f354d44df9764

20 in → 2 out540.0250 XPM2.97 KB

ALPhqDWq…8HHmYGkx AbAtAwQE…JYri7z8Y

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.

8.672 × 10⁹⁷(98-digit number)

86726830521104643159…54425397097493299199

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

8.672 × 10⁹⁷(98-digit number)

86726830521104643159…54425397097493299199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.672 × 10⁹⁷(98-digit number)

86726830521104643159…54425397097493299201

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

1.734 × 10⁹⁸(99-digit number)

17345366104220928631…08850794194986598399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.734 × 10⁹⁸(99-digit number)

17345366104220928631…08850794194986598401

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

3.469 × 10⁹⁸(99-digit number)

34690732208441857263…17701588389973196799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.469 × 10⁹⁸(99-digit number)

34690732208441857263…17701588389973196801

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

6.938 × 10⁹⁸(99-digit number)

69381464416883714527…35403176779946393599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.938 × 10⁹⁸(99-digit number)

69381464416883714527…35403176779946393601

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

1.387 × 10⁹⁹(100-digit number)

13876292883376742905…70806353559892787199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.387 × 10⁹⁹(100-digit number)

13876292883376742905…70806353559892787201

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

2.775 × 10⁹⁹(100-digit number)

27752585766753485810…41612707119785574399

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 #3,099,034

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