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Home/Chain Registry/Block #2,133,282

Block #2,133,282

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2017, 9:49:25 AM Β· Difficulty 10.9098 Β· 4,712,007 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b14b1495355e2944db6258f8317aa43264993d9aeac5c43f7a6277f30d5210c1
View on Chainz β†—

Difficulty

10.909782

Transactions

1

Size

200 B

Version

2

Bits

0ae8e778

Nonce

165,753,432

Timestamp

5/26/2017, 9:49:25 AM

Confirmations

4,712,007

Merkle Root

c266c30eec3d21527269f8f42e94d35c90b77b06d2f572bcc9b72a5b81865957
Transactions (1)
Coinbasec266c30eec3d21…b72a5b81865957
1 in β†’ 1 out8.3900 XPM110 B
ATwLH32w…w3fZy34L
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.

2.074 Γ— 10⁹⁴(95-digit number)
20748141756929505088…10217937850063002220
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
2.074 Γ— 10⁹⁴(95-digit number)
20748141756929505088…10217937850063002221
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.149 Γ— 10⁹⁴(95-digit number)
41496283513859010176…20435875700126004441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.299 Γ— 10⁹⁴(95-digit number)
82992567027718020352…40871751400252008881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.659 Γ— 10⁹⁡(96-digit number)
16598513405543604070…81743502800504017761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.319 Γ— 10⁹⁡(96-digit number)
33197026811087208140…63487005601008035521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.639 Γ— 10⁹⁡(96-digit number)
66394053622174416281…26974011202016071041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.327 Γ— 10⁹⁢(97-digit number)
13278810724434883256…53948022404032142081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.655 Γ— 10⁹⁢(97-digit number)
26557621448869766512…07896044808064284161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.311 Γ— 10⁹⁢(97-digit number)
53115242897739533025…15792089616128568321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.062 Γ— 10⁹⁷(98-digit number)
10623048579547906605…31584179232257136641
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
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 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 2133282

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 b14b1495355e2944db6258f8317aa43264993d9aeac5c43f7a6277f30d5210c1

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 #2,133,282 on Chainz β†—
Circulating Supply:58,006,749 XPMΒ·at block #6,845,288 Β· updates every 60s
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