Block #2,585,390

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/25/2018, 7:14:40 PM · Difficulty 11.2518 · 4,257,733 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

56c4a5ff6a2cca79bd65372e34ff53d0f81b63671a9b922cdf817d0230636593

View on Chainz ↗

Height

#2,585,390

Difficulty

11.251787

Transactions

Size

891 B

Version

Bits

0b407517

Nonce

538,697,069

Timestamp

3/25/2018, 7:14:40 PM

Confirmations

4,257,733

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

958c5d021faa7a3cd90ad49536394b28ccee4bfd2e6f4805363c65dd10f42e6e

Transactions (4)

Coinbase85952b4d6f3ae4…e53e1d52a9278b

1 in → 1 out7.9200 XPM110 B

Adqah8zh…1WwoHJ9t

29dcb8596bbd5b…67f78798dd55e5

2 in → 2 out16.1500 XPM306 B

AdMtrT7m…zgeRbAcK AGXNtC81…A8fDbzn4

a0376604fde78d…26d24ae90dfae7

1 in → 2 out8.0700 XPM192 B

ANxNfXmZ…4p5PaHCM ARPLQ6Lc…6EQsb6t1

ed96fd2b897e53…b68835a9019478

1 in → 2 out8.0700 XPM193 B

AJeVuWtN…RBAisDqp AMjZ87GH…cvurqAXE

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.

2.258 × 10⁹⁵(96-digit number)

22586271809561760426…22114925979043852799

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

2.258 × 10⁹⁵(96-digit number)

22586271809561760426…22114925979043852799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.258 × 10⁹⁵(96-digit number)

22586271809561760426…22114925979043852801

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

4.517 × 10⁹⁵(96-digit number)

45172543619123520853…44229851958087705599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.517 × 10⁹⁵(96-digit number)

45172543619123520853…44229851958087705601

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

9.034 × 10⁹⁵(96-digit number)

90345087238247041707…88459703916175411199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.034 × 10⁹⁵(96-digit number)

90345087238247041707…88459703916175411201

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

1.806 × 10⁹⁶(97-digit number)

18069017447649408341…76919407832350822399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.806 × 10⁹⁶(97-digit number)

18069017447649408341…76919407832350822401

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

3.613 × 10⁹⁶(97-digit number)

36138034895298816683…53838815664701644799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.613 × 10⁹⁶(97-digit number)

36138034895298816683…53838815664701644801

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

7.227 × 10⁹⁶(97-digit number)

72276069790597633366…07677631329403289599

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 #2,585,390

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