XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,865,322

Block #2,865,322

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/3/2018, 10:09:56 AM Β· Difficulty 11.6704 Β· 3,974,155 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
4e7465c894e96d330d356e853ac90ffeb46b3bdf6ea3c937493a58bb6c1cfff0
View on Chainz β†—

Difficulty

11.670446

Transactions

1

Size

199 B

Version

2

Bits

0baba260

Nonce

326,576,353

Timestamp

10/3/2018, 10:09:56 AM

Confirmations

3,974,155

Merkle Root

81a4645fd6134d5a1b2e58917d5db2f6ea13319a1cec27277d62879203ac4c4e
Transactions (1)
Coinbase81a4645fd6134d…62879203ac4c4e
1 in β†’ 1 out7.3300 XPM109 B
AUMQRepm…tAfKmdW1
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.935 Γ— 10⁹⁴(95-digit number)
69354447878844412587…48442333967785987840
Discovered Prime Numbers
p_k = 2^k Γ— 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.

1
origin + 1
6.935 Γ— 10⁹⁴(95-digit number)
69354447878844412587…48442333967785987841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.387 Γ— 10⁹⁡(96-digit number)
13870889575768882517…96884667935571975681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.774 Γ— 10⁹⁡(96-digit number)
27741779151537765035…93769335871143951361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.548 Γ— 10⁹⁡(96-digit number)
55483558303075530070…87538671742287902721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.109 Γ— 10⁹⁢(97-digit number)
11096711660615106014…75077343484575805441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.219 Γ— 10⁹⁢(97-digit number)
22193423321230212028…50154686969151610881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.438 Γ— 10⁹⁢(97-digit number)
44386846642460424056…00309373938303221761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.877 Γ— 10⁹⁢(97-digit number)
88773693284920848112…00618747876606443521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.775 Γ— 10⁹⁷(98-digit number)
17754738656984169622…01237495753212887041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.550 Γ— 10⁹⁷(98-digit number)
35509477313968339244…02474991506425774081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.101 Γ— 10⁹⁷(98-digit number)
71018954627936678489…04949983012851548161
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2865322

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 4e7465c894e96d330d356e853ac90ffeb46b3bdf6ea3c937493a58bb6c1cfff0

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 β†’ Debug Window β†’ 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 #2,865,322 on Chainz β†—
Circulating Supply:57,960,108 XPMΒ·at block #6,839,476 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy