Block #2,581,317

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/23/2018, 5:17:12 PM · Difficulty 11.0734 · 4,259,515 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0c557748c48ac15d7a5f0e049bf5697a137fbfbfa7ebe554edf0f481672fad12

View on Chainz ↗

Height

#2,581,317

Difficulty

11.073435

Transactions

Size

1.19 KB

Version

Bits

0b12ccab

Nonce

1,214,060,391

Timestamp

3/23/2018, 5:17:12 PM

Confirmations

4,259,515

Mined by

⛏️ P2SHAS4VK4mEQDnsZbf1n45Uf8FZ5skEQJbvHX

Merkle Root

062828894a1819b4991a6cd92fb3bfa57b1ab9fd295756aca7e6de594a0fb6be

Transactions (4)

Coinbaseac30f58df3731e…5b5f0e73db3b34

1 in → 1 out8.1700 XPM110 B

AS4VK4mE…kEQJbvHX

ab876edc8d03ec…a292004feb50ae

2 in → 2 out14.7600 XPM339 B

ANepN4vB…ZcMWhc7E AGjVwKtt…rb3DXPCA

51fd1ad7f18343…52870c27084bc3

2 in → 2 out11.2600 XPM338 B

AR3cBEuE…9vc8keub Aecb8e8N…t82ZAf4K

4c08c6169964ed…7e6587a093d919

2 in → 2 out13.0200 XPM340 B

AcXtoaKv…4oXYPT9v AQfGP1Np…7h4jMazz

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.

3.587 × 10⁹⁹(100-digit number)

35872470500538383593…88887764939290705919

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

3.587 × 10⁹⁹(100-digit number)

35872470500538383593…88887764939290705919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.587 × 10⁹⁹(100-digit number)

35872470500538383593…88887764939290705921

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

7.174 × 10⁹⁹(100-digit number)

71744941001076767186…77775529878581411839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.174 × 10⁹⁹(100-digit number)

71744941001076767186…77775529878581411841

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

1.434 × 10¹⁰⁰(101-digit number)

14348988200215353437…55551059757162823679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.434 × 10¹⁰⁰(101-digit number)

14348988200215353437…55551059757162823681

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

2.869 × 10¹⁰⁰(101-digit number)

28697976400430706874…11102119514325647359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.869 × 10¹⁰⁰(101-digit number)

28697976400430706874…11102119514325647361

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

5.739 × 10¹⁰⁰(101-digit number)

57395952800861413749…22204239028651294719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.739 × 10¹⁰⁰(101-digit number)

57395952800861413749…22204239028651294721

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

1.147 × 10¹⁰¹(102-digit number)

11479190560172282749…44408478057302589439

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 #2,581,317

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