Block #2,726,225

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/29/2018, 5:34:48 AM · Difficulty 11.6245 · 4,114,677 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1b95672cb148acc50f7264d7400972676c639f3b4d7b12ec02faaee9b2657026

View on Chainz ↗

Height

#2,726,225

Difficulty

11.624530

Transactions

Size

1.82 KB

Version

Bits

0b9fe13a

Nonce

671,913,191

Timestamp

6/29/2018, 5:34:48 AM

Confirmations

4,114,677

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

c5e492e2ae1a871f34065aef6011e308e2149359a3220059ce8b1f1e7f8b878e

Transactions (5)

Coinbase5e69c1fb38a571…f3d115b5edf1b7

1 in → 1 out7.4300 XPM110 B

AZtxQr2F…7grUWrUz

ce633b09d9a1f2…43a24c7f79656d

5 in → 2 out36.9900 XPM649 B

AWp4iAg7…FUBLEm8x Ac2TdZi8…H7fcv2pg

a93f7a9452c1d4…7733a2af4f7c01

1 in → 2 out7.3900 XPM191 B

ALa9Z6aQ…Y9heUeLa AL1yjimw…R21ALN7h

6dedfeafaac9c2…382ff14c663dbe

2 in → 2 out10.7685 XPM340 B

AKmW9Tje…kCLwCrwy AXugfzbx…diuqujX8

c6aac242333731…60b0fec5d68304

3 in → 2 out10.1099 XPM489 B

AGzrd4MM…7HC9qVLn ANKDUHpK…g1RL2rfr

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.

2.155 × 10⁹³(94-digit number)

21558674626510112187…85115055558242062919

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

2.155 × 10⁹³(94-digit number)

21558674626510112187…85115055558242062919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.155 × 10⁹³(94-digit number)

21558674626510112187…85115055558242062921

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

4.311 × 10⁹³(94-digit number)

43117349253020224375…70230111116484125839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.311 × 10⁹³(94-digit number)

43117349253020224375…70230111116484125841

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

8.623 × 10⁹³(94-digit number)

86234698506040448750…40460222232968251679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.623 × 10⁹³(94-digit number)

86234698506040448750…40460222232968251681

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

1.724 × 10⁹⁴(95-digit number)

17246939701208089750…80920444465936503359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.724 × 10⁹⁴(95-digit number)

17246939701208089750…80920444465936503361

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

3.449 × 10⁹⁴(95-digit number)

34493879402416179500…61840888931873006719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.449 × 10⁹⁴(95-digit number)

34493879402416179500…61840888931873006721

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

6.898 × 10⁹⁴(95-digit number)

68987758804832359000…23681777863746013439

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 #2,726,225

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