Block #2,572,326

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/18/2018, 1:15:51 PM · Difficulty 10.9948 · 4,269,754 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e26a4a6b4f3c2041e95d0124316022ad047d46f971692d30a7bea7e8cba98d79

View on Chainz ↗

Height

#2,572,326

Difficulty

10.994840

Transactions

Size

423 B

Version

Bits

0afeadd4

Nonce

1,080,028,512

Timestamp

3/18/2018, 1:15:51 PM

Confirmations

4,269,754

Mined by

⛏️ P2SHAcQkJYsDQrv1qekFveykCgPnx34pUSttrD

Merkle Root

f941f26cea070dd6f88e2563377557003ce5ea28a3c397cef19b0ae15bccc4c0

Transactions (2)

Coinbase7f3b64731e21d0…09aba6eefa9aa1

1 in → 1 out8.2700 XPM109 B

AcQkJYsD…4pUSttrD

f9b1864ca5682f…c45f6ebcdb2577

1 in → 2 out13131.7705 XPM225 B

AR7nnUEq…KctfCYg8 ATLsJ91u…uwZa9Mer

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.

7.076 × 10⁹¹(92-digit number)

70761594133540157995…44340891823339397999

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

7.076 × 10⁹¹(92-digit number)

70761594133540157995…44340891823339397999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.076 × 10⁹¹(92-digit number)

70761594133540157995…44340891823339398001

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

1.415 × 10⁹²(93-digit number)

14152318826708031599…88681783646678795999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.415 × 10⁹²(93-digit number)

14152318826708031599…88681783646678796001

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

2.830 × 10⁹²(93-digit number)

28304637653416063198…77363567293357591999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.830 × 10⁹²(93-digit number)

28304637653416063198…77363567293357592001

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

5.660 × 10⁹²(93-digit number)

56609275306832126396…54727134586715183999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.660 × 10⁹²(93-digit number)

56609275306832126396…54727134586715184001

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

1.132 × 10⁹³(94-digit number)

11321855061366425279…09454269173430367999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.132 × 10⁹³(94-digit number)

11321855061366425279…09454269173430368001

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

2.264 × 10⁹³(94-digit number)

22643710122732850558…18908538346860735999

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 #2,572,326

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