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Home/Chain Registry/Block #2,281,995

Block #2,281,995

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/4/2017, 11:00:10 AM Β· Difficulty 10.9557 Β· 4,544,052 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0edc84d8773cafcd44375e3571d0840852e87f281088d04ca15b359d536a4d71
View on Chainz β†—

Difficulty

10.955672

Transactions

1

Size

200 B

Version

2

Bits

0af4a6e5

Nonce

1,206,360,995

Timestamp

9/4/2017, 11:00:10 AM

Confirmations

4,544,052

Merkle Root

a0b5cff3197a5e3aaa7e57702dfb715afec6dcf709e95fb94afab2c9150cf48f
Transactions (1)
Coinbasea0b5cff3197a5e…fab2c9150cf48f
1 in β†’ 1 out8.3200 XPM110 B
AaeC99qH…Yrw12N7F
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.

2.307 Γ— 10⁹⁴(95-digit number)
23076457607862150573…62818682352947587520
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
2.307 Γ— 10⁹⁴(95-digit number)
23076457607862150573…62818682352947587521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.615 Γ— 10⁹⁴(95-digit number)
46152915215724301147…25637364705895175041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.230 Γ— 10⁹⁴(95-digit number)
92305830431448602294…51274729411790350081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.846 Γ— 10⁹⁡(96-digit number)
18461166086289720458…02549458823580700161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.692 Γ— 10⁹⁡(96-digit number)
36922332172579440917…05098917647161400321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.384 Γ— 10⁹⁡(96-digit number)
73844664345158881835…10197835294322800641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.476 Γ— 10⁹⁢(97-digit number)
14768932869031776367…20395670588645601281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.953 Γ— 10⁹⁢(97-digit number)
29537865738063552734…40791341177291202561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.907 Γ— 10⁹⁢(97-digit number)
59075731476127105468…81582682354582405121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.181 Γ— 10⁹⁷(98-digit number)
11815146295225421093…63165364709164810241
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 2281995

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 0edc84d8773cafcd44375e3571d0840852e87f281088d04ca15b359d536a4d71

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 #2,281,995 on Chainz β†—
Circulating Supply:57,852,502 XPMΒ·at block #6,826,046 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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