Home/Chain Registry/Block #2,821,547

Block #2,821,547

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/2/2018, 3:22:25 PM · Difficulty 11.7031 · 4,021,434 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76880d7de0e2d22bed67e24589bbc8ab5c8df6c0749b5103b6639a528cf3abd4

View on Chainz ↗

Height

#2,821,547

Difficulty

11.703093

Transactions

Size

950 B

Version

Bits

0bb3fded

Nonce

1,006,836,911

Timestamp

9/2/2018, 3:22:25 PM

Confirmations

4,021,434

Merkle Root

e03f7226bdad8e09cacf3a0534aa8ede0768a45792da8af0e380494d72bcb28a

Transactions (3)

Coinbase9df715b5960a38…6a379ff3778e2e

1 in → 1 out7.3100 XPM110 B

AZtxQr2F…7grUWrUz

c58e2725935265…1e27bb954c8b74

2 in → 2 out6.5700 XPM376 B

ALzge2Pu…V9V1hcPi AKkxX1JN…RsYBzK96

f504c4cf4c008c…caea0c6f8f9ebd

2 in → 2 out6.5700 XPM374 B

AeqVFBCX…AXEH1UFP ALkY5jiv…STtdwyQs

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.

1.058 × 10⁹⁴(95-digit number)

10581606911529169778…45824146439665419520

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

1.058 × 10⁹⁴(95-digit number)

10581606911529169778…45824146439665419519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.058 × 10⁹⁴(95-digit number)

10581606911529169778…45824146439665419521

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

2.116 × 10⁹⁴(95-digit number)

21163213823058339557…91648292879330839039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.116 × 10⁹⁴(95-digit number)

21163213823058339557…91648292879330839041

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

4.232 × 10⁹⁴(95-digit number)

42326427646116679114…83296585758661678079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.232 × 10⁹⁴(95-digit number)

42326427646116679114…83296585758661678081

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

8.465 × 10⁹⁴(95-digit number)

84652855292233358229…66593171517323356159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.465 × 10⁹⁴(95-digit number)

84652855292233358229…66593171517323356161

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

1.693 × 10⁹⁵(96-digit number)

16930571058446671645…33186343034646712319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.693 × 10⁹⁵(96-digit number)

16930571058446671645…33186343034646712321

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

3.386 × 10⁹⁵(96-digit number)

33861142116893343291…66372686069293424639

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 2821547

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 76880d7de0e2d22bed67e24589bbc8ab5c8df6c0749b5103b6639a528cf3abd4

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 #2,821,547 on Chainz ↗

Block #2,821,547

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