Home/Chain Registry/Block #2,526,455

Block #2,526,455

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/18/2018, 4:34:09 AM · Difficulty 10.9839 · 4,316,818 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e589552d5e98cef191f6dc1cc8bb57bcc1aff33541179837710866c65471d7aa

View on Chainz ↗

Height

#2,526,455

Difficulty

10.983868

Transactions

Size

1.65 KB

Version

Bits

0afbdebe

Nonce

953,643,799

Timestamp

2/18/2018, 4:34:09 AM

Confirmations

4,316,818

Merkle Root

bc3ae5ac6c9972df66c326bb02549a5a5cf988ebd15a71d57d32ad054d9afab1

Transactions (3)

Coinbase054c2773f8fbdf…7789c8cca88aa5

1 in → 1 out8.3000 XPM110 B

AbMLVeFy…Wr3Zxwpa

7526978937757d…72ac7b13bfb47c

3 in → 2 out47.0267 XPM524 B

AHXGHJCA…rcSdXGV2 AbS8LcRV…bYCP4MhW

83edf2f5a3989a…c9f8fd2acd4180

6 in → 2 out29.6736 XPM966 B

AWazzBRK…EVXpASRg AcyKfXd3…Swm8Q3zi

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.

4.971 × 10⁹⁴(95-digit number)

49714874062023918245…43001227059975790880

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

4.971 × 10⁹⁴(95-digit number)

49714874062023918245…43001227059975790879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.971 × 10⁹⁴(95-digit number)

49714874062023918245…43001227059975790881

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

9.942 × 10⁹⁴(95-digit number)

99429748124047836490…86002454119951581759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.942 × 10⁹⁴(95-digit number)

99429748124047836490…86002454119951581761

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

1.988 × 10⁹⁵(96-digit number)

19885949624809567298…72004908239903163519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.988 × 10⁹⁵(96-digit number)

19885949624809567298…72004908239903163521

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

3.977 × 10⁹⁵(96-digit number)

39771899249619134596…44009816479806327039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.977 × 10⁹⁵(96-digit number)

39771899249619134596…44009816479806327041

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

7.954 × 10⁹⁵(96-digit number)

79543798499238269192…88019632959612654079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.954 × 10⁹⁵(96-digit number)

79543798499238269192…88019632959612654081

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

1.590 × 10⁹⁶(97-digit number)

15908759699847653838…76039265919225308159

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.

View full Prime Chain Discovery page →

★★★☆☆

Rarity

RareChain length 11

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 2526455

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock e589552d5e98cef191f6dc1cc8bb57bcc1aff33541179837710866c65471d7aa

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,526,455 on Chainz ↗

Block #2,526,455

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