Block #2,830,611

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/8/2018, 6:29:15 PM · Difficulty 11.7170 · 4,002,602 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1f4f19993eb917fadbfd39d1cdcc51f8ef6cc75b09dc08bcf398eaf1de592f1b

View on Chainz ↗

Height

#2,830,611

Difficulty

11.717032

Transactions

Size

428 B

Version

Bits

0bb78f64

Nonce

41,643,017

Timestamp

9/8/2018, 6:29:15 PM

Confirmations

4,002,602

Mined by

⛏️ P2SHASeuEimfpZoN7ghbxoVYkuVtdfm3Z5TgVr

Merkle Root

065c787c02c226cbe3091372b2e7334fb23083e222b9a63ba6bb7799032d7121

Transactions (2)

Coinbase666683e7a37b7d…75ba39af46e3cc

1 in → 1 out7.2800 XPM110 B

ASeuEimf…m3Z5TgVr

d67c505d7b527d…5d1000bfe1949e

1 in → 2 out7160.7290 XPM226 B

AePUrSda…VggJsMZn AKQvFqFd…yT442Sim

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.

4.208 × 10⁹⁸(99-digit number)

42089924112154983587…86665733800733204479

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

4.208 × 10⁹⁸(99-digit number)

42089924112154983587…86665733800733204479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.208 × 10⁹⁸(99-digit number)

42089924112154983587…86665733800733204481

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

8.417 × 10⁹⁸(99-digit number)

84179848224309967175…73331467601466408959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.417 × 10⁹⁸(99-digit number)

84179848224309967175…73331467601466408961

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

1.683 × 10⁹⁹(100-digit number)

16835969644861993435…46662935202932817919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.683 × 10⁹⁹(100-digit number)

16835969644861993435…46662935202932817921

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

3.367 × 10⁹⁹(100-digit number)

33671939289723986870…93325870405865635839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.367 × 10⁹⁹(100-digit number)

33671939289723986870…93325870405865635841

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

6.734 × 10⁹⁹(100-digit number)

67343878579447973740…86651740811731271679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.734 × 10⁹⁹(100-digit number)

67343878579447973740…86651740811731271681

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

1.346 × 10¹⁰⁰(101-digit number)

13468775715889594748…73303481623462543359

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 #2,830,611

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