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Block #2,268,586

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/26/2017, 8:38:32 AM Β· Difficulty 10.9525 Β· 4,562,408 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2a34d253b05ab5ead741b038d114939530a1d50f996548ed57dbd72cc02f00d0
View on Chainz β†—

Difficulty

10.952463

Transactions

1

Size

201 B

Version

2

Bits

0af3d49b

Nonce

683,883,418

Timestamp

8/26/2017, 8:38:32 AM

Confirmations

4,562,408

Merkle Root

851e5ccedcfb41f48510eb03f1596d70b1817c9f5c93f62f229b4277bd76a9d4
Transactions (1)
Coinbase851e5ccedcfb41…9b4277bd76a9d4
1 in β†’ 1 out8.3200 XPM110 B
AVri5KYw…FbAPyDhg
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.

4.220 Γ— 10⁹⁢(97-digit number)
42200462999449342444…94524347124846515200
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
4.220 Γ— 10⁹⁢(97-digit number)
42200462999449342444…94524347124846515201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.440 Γ— 10⁹⁢(97-digit number)
84400925998898684889…89048694249693030401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.688 Γ— 10⁹⁷(98-digit number)
16880185199779736977…78097388499386060801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.376 Γ— 10⁹⁷(98-digit number)
33760370399559473955…56194776998772121601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.752 Γ— 10⁹⁷(98-digit number)
67520740799118947911…12389553997544243201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.350 Γ— 10⁹⁸(99-digit number)
13504148159823789582…24779107995088486401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.700 Γ— 10⁹⁸(99-digit number)
27008296319647579164…49558215990176972801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.401 Γ— 10⁹⁸(99-digit number)
54016592639295158329…99116431980353945601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.080 Γ— 10⁹⁹(100-digit number)
10803318527859031665…98232863960707891201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.160 Γ— 10⁹⁹(100-digit number)
21606637055718063331…96465727921415782401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.321 Γ— 10⁹⁹(100-digit number)
43213274111436126663…92931455842831564801
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 2268586

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 2a34d253b05ab5ead741b038d114939530a1d50f996548ed57dbd72cc02f00d0

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 #2,268,586 on Chainz β†—
Circulating Supply:57,892,093 XPMΒ·at block #6,830,993 Β· updates every 60s
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