Home/Chain Registry/Block #2,559,674

Block #2,559,674

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2018, 3:39:45 AM · Difficulty 10.9919 · 4,273,133 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b61a569c124067028c32f795be38e2bfce15cccf4f9a7482d105d2287a05c29

View on Chainz ↗

Height

#2,559,674

Difficulty

10.991876

Transactions

Size

200 B

Version

Bits

0afdeb9e

Nonce

314,669,776

Timestamp

3/11/2018, 3:39:45 AM

Confirmations

4,273,133

Merkle Root

2fc8ee8504c6013cbc4d1a451f9e896b06a207a63aa40d850de9bd1563d2aa4a

Transactions (1)

Coinbase2fc8ee8504c601…e9bd1563d2aa4a

1 in → 1 out8.2600 XPM109 B

AJZo55jr…YSPk8sQH

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.

1.356 × 10⁹⁷(98-digit number)

13560759771047112221…86108167319207895040

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

1.356 × 10⁹⁷(98-digit number)

13560759771047112221…86108167319207895039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.356 × 10⁹⁷(98-digit number)

13560759771047112221…86108167319207895041

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

2.712 × 10⁹⁷(98-digit number)

27121519542094224443…72216334638415790079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.712 × 10⁹⁷(98-digit number)

27121519542094224443…72216334638415790081

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

5.424 × 10⁹⁷(98-digit number)

54243039084188448887…44432669276831580159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.424 × 10⁹⁷(98-digit number)

54243039084188448887…44432669276831580161

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

1.084 × 10⁹⁸(99-digit number)

10848607816837689777…88865338553663160319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.084 × 10⁹⁸(99-digit number)

10848607816837689777…88865338553663160321

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

2.169 × 10⁹⁸(99-digit number)

21697215633675379554…77730677107326320639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.169 × 10⁹⁸(99-digit number)

21697215633675379554…77730677107326320641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 2559674

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 2b61a569c124067028c32f795be38e2bfce15cccf4f9a7482d105d2287a05c29

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 #2,559,674 on Chainz ↗

Block #2,559,674

Cookie Preferences