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Block #2,291,572

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/11/2017, 4:27:34 AM Β· Difficulty 10.9550 Β· 4,541,796 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3015cd26a6bfdacddd3de437076addde2bd6823151dfc0496909d5112e2ae6c2
View on Chainz β†—

Difficulty

10.954981

Transactions

1

Size

200 B

Version

2

Bits

0af4799f

Nonce

2,122,630,449

Timestamp

9/11/2017, 4:27:34 AM

Confirmations

4,541,796

Merkle Root

cac298673547e4f79ba4a3207ccc9a18056cc89dcc953391456cc39af03b6ec9
Transactions (1)
Coinbasecac298673547e4…6cc39af03b6ec9
1 in β†’ 1 out8.3200 XPM110 B
ANJNB4mS…i1nciMZG
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.

7.488 Γ— 10⁹³(94-digit number)
74880139974533249160…37589755269235373400
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
7.488 Γ— 10⁹³(94-digit number)
74880139974533249160…37589755269235373401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.497 Γ— 10⁹⁴(95-digit number)
14976027994906649832…75179510538470746801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.995 Γ— 10⁹⁴(95-digit number)
29952055989813299664…50359021076941493601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.990 Γ— 10⁹⁴(95-digit number)
59904111979626599328…00718042153882987201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.198 Γ— 10⁹⁡(96-digit number)
11980822395925319865…01436084307765974401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.396 Γ— 10⁹⁡(96-digit number)
23961644791850639731…02872168615531948801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.792 Γ— 10⁹⁡(96-digit number)
47923289583701279462…05744337231063897601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.584 Γ— 10⁹⁡(96-digit number)
95846579167402558925…11488674462127795201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.916 Γ— 10⁹⁢(97-digit number)
19169315833480511785…22977348924255590401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.833 Γ— 10⁹⁢(97-digit number)
38338631666961023570…45954697848511180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.667 Γ— 10⁹⁢(97-digit number)
76677263333922047140…91909395697022361601
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 2291572

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 3015cd26a6bfdacddd3de437076addde2bd6823151dfc0496909d5112e2ae6c2

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 #2,291,572 on Chainz β†—
Circulating Supply:57,911,141 XPMΒ·at block #6,833,367 Β· updates every 60s
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