Block #2,818,001

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/31/2018, 6:10:52 AM · Difficulty 11.6962 · 4,023,536 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

08aa1868de35f55e5b15b707b6fd7c3c331fb34df4baed311dd6173b0b376e2a

View on Chainz ↗

Height

#2,818,001

Difficulty

11.696196

Transactions

Size

847 B

Version

Bits

0bb239ea

Nonce

561,325,227

Timestamp

8/31/2018, 6:10:52 AM

Confirmations

4,023,536

Mined by

⛏️ P2SHALiUkHwc19SyWDfmBTLPWc6Ej82Qp5KRyN

Merkle Root

a75489c575624f54263dde9db7d82e5ba258eee8839adce0e302732bcded1cf4

Transactions (3)

Coinbasef213903215112f…40e0a35886238c

1 in → 1 out7.3200 XPM110 B

ALiUkHwc…2Qp5KRyN

7d3ccaf5193c2f…99ff2ab942475b

2 in → 2 out14.6400 XPM307 B

APpE9HSp…a9J4XSoT AR9ZodTU…o7SubEUG

d02fc28a105fed…6379537e136c04

2 in → 2 out11.9400 XPM340 B

AJH5DjFu…ZXbzd13Y AZx4Xx9S…ah1QAhSN

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.

6.537 × 10⁹³(94-digit number)

65377517858497608232…64892567412776685109

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

6.537 × 10⁹³(94-digit number)

65377517858497608232…64892567412776685109

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.537 × 10⁹³(94-digit number)

65377517858497608232…64892567412776685111

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

1.307 × 10⁹⁴(95-digit number)

13075503571699521646…29785134825553370219

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.307 × 10⁹⁴(95-digit number)

13075503571699521646…29785134825553370221

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

2.615 × 10⁹⁴(95-digit number)

26151007143399043292…59570269651106740439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.615 × 10⁹⁴(95-digit number)

26151007143399043292…59570269651106740441

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

5.230 × 10⁹⁴(95-digit number)

52302014286798086585…19140539302213480879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.230 × 10⁹⁴(95-digit number)

52302014286798086585…19140539302213480881

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

1.046 × 10⁹⁵(96-digit number)

10460402857359617317…38281078604426961759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.046 × 10⁹⁵(96-digit number)

10460402857359617317…38281078604426961761

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

2.092 × 10⁹⁵(96-digit number)

20920805714719234634…76562157208853923519

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 #2,818,001

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