Block #2,750,199

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/15/2018, 4:15:10 PM · Difficulty 11.6466 · 4,082,835 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0ee496ff1e0d91a076039a91f7395c86a88b211f51e76f89de4cb9586f90d881

View on Chainz ↗

Height

#2,750,199

Difficulty

11.646600

Transactions

Size

722 B

Version

Bits

0ba5879b

Nonce

104,115,383

Timestamp

7/15/2018, 4:15:10 PM

Confirmations

4,082,835

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

ff4123f2a79bb09208ce4aac16a5d7af796fc328d56cc7bd43243a86a156be91

Transactions (2)

Coinbase5d45c63cad3fad…f9d7b94a98da1d

1 in → 1 out7.3700 XPM110 B

AZtxQr2F…7grUWrUz

b16ab8a96e7b28…f37c3966f05dc7

3 in → 2 out251.8893 XPM522 B

AMacMFhM…iFNVuut4 AGqdTQPB…pd7Mp3tu

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.

3.902 × 10⁹⁵(96-digit number)

39021881748095711845…09234229113097748479

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

3.902 × 10⁹⁵(96-digit number)

39021881748095711845…09234229113097748479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.902 × 10⁹⁵(96-digit number)

39021881748095711845…09234229113097748481

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

7.804 × 10⁹⁵(96-digit number)

78043763496191423691…18468458226195496959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.804 × 10⁹⁵(96-digit number)

78043763496191423691…18468458226195496961

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

1.560 × 10⁹⁶(97-digit number)

15608752699238284738…36936916452390993919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.560 × 10⁹⁶(97-digit number)

15608752699238284738…36936916452390993921

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

3.121 × 10⁹⁶(97-digit number)

31217505398476569476…73873832904781987839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.121 × 10⁹⁶(97-digit number)

31217505398476569476…73873832904781987841

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

6.243 × 10⁹⁶(97-digit number)

62435010796953138953…47747665809563975679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.243 × 10⁹⁶(97-digit number)

62435010796953138953…47747665809563975681

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

1.248 × 10⁹⁷(98-digit number)

12487002159390627790…95495331619127951359

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 #2,750,199

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