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Block #212,282

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/16/2013, 4:51:58 AM Β· Difficulty 9.9186 Β· 6,614,105 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5e0277cf365cd29f82b33a769f8046c509349413525c81d8e317c3a60d91fd08
View on Chainz β†—

Height

#212,282

Difficulty

9.918597

Transactions

1

Size

199 B

Version

2

Bits

09eb2926

Nonce

7,781

Timestamp

10/16/2013, 4:51:58 AM

Confirmations

6,614,105

Merkle Root

e13bd67cc50f97f32df4dad845b08110f611b3a85a1b9205515d2ef7dd2a41fa
Transactions (1)
Coinbasee13bd67cc50f97…5d2ef7dd2a41fa
1 in β†’ 1 out10.1500 XPM109 B
AUaxt9ro…AcE93k1m
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.

8.418 Γ— 10⁹³(94-digit number)
84180877119034943899…04639390919692275040
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
8.418 Γ— 10⁹³(94-digit number)
84180877119034943899…04639390919692275039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.683 Γ— 10⁹⁴(95-digit number)
16836175423806988779…09278781839384550079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.367 Γ— 10⁹⁴(95-digit number)
33672350847613977559…18557563678769100159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.734 Γ— 10⁹⁴(95-digit number)
67344701695227955119…37115127357538200319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.346 Γ— 10⁹⁡(96-digit number)
13468940339045591023…74230254715076400639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.693 Γ— 10⁹⁡(96-digit number)
26937880678091182047…48460509430152801279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.387 Γ— 10⁹⁡(96-digit number)
53875761356182364095…96921018860305602559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.077 Γ— 10⁹⁢(97-digit number)
10775152271236472819…93842037720611205119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.155 Γ— 10⁹⁢(97-digit number)
21550304542472945638…87684075441222410239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First 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
CommonChain length 9
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 212282

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 5e0277cf365cd29f82b33a769f8046c509349413525c81d8e317c3a60d91fd08

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 #212,282 on Chainz β†—
Circulating Supply:57,855,234 XPMΒ·at block #6,826,386 Β· updates every 60s
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