Block #2,802,988

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/21/2018, 2:47:26 AM · Difficulty 11.6699 · 4,028,655 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f5be93a2960726fd67cd52965b500fba45d195fb0df78fd24afb4f51ce2d843e

View on Chainz ↗

Height

#2,802,988

Difficulty

11.669941

Transactions

Size

4.60 KB

Version

Bits

0bab8140

Nonce

2,049,531,957

Timestamp

8/21/2018, 2:47:26 AM

Confirmations

4,028,655

Mined by

⛏️ P2SHAPvVwaeS48GJTUmzj5s2QV9P4jHtjnwu98

Merkle Root

4f1190929b908f1e7117f74a5726fa9c6cfcba71814a9bcb4dc3ae30f703ab08

Transactions (2)

Coinbase5d5b55f46151d2…bba5bb8cd032c4

1 in → 1 out7.3800 XPM109 B

APvVwaeS…Htjnwu98

1154cb914d246d…47f57b2c9cb1c7

30 in → 2 out15697.8200 XPM4.41 KB

AeLWFbtN…BdxnmXEU AQSehNCS…tBaLHmvQ

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.

2.423 × 10⁹⁵(96-digit number)

24234063744132828188…30586547797575057919

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

2.423 × 10⁹⁵(96-digit number)

24234063744132828188…30586547797575057919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.423 × 10⁹⁵(96-digit number)

24234063744132828188…30586547797575057921

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

4.846 × 10⁹⁵(96-digit number)

48468127488265656376…61173095595150115839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.846 × 10⁹⁵(96-digit number)

48468127488265656376…61173095595150115841

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

9.693 × 10⁹⁵(96-digit number)

96936254976531312753…22346191190300231679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.693 × 10⁹⁵(96-digit number)

96936254976531312753…22346191190300231681

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

1.938 × 10⁹⁶(97-digit number)

19387250995306262550…44692382380600463359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.938 × 10⁹⁶(97-digit number)

19387250995306262550…44692382380600463361

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

3.877 × 10⁹⁶(97-digit number)

38774501990612525101…89384764761200926719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.877 × 10⁹⁶(97-digit number)

38774501990612525101…89384764761200926721

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

7.754 × 10⁹⁶(97-digit number)

77549003981225050203…78769529522401853439

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 #2,802,988

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