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Block #212,914

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/16/2013, 2:18:57 PM Β· Difficulty 9.9196 Β· 6,614,210 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1d4eb952c2631cae21ea29665c9f0dbde7de99f9111ae98e1f2ac6569e38fe8b
View on Chainz β†—

Height

#212,914

Difficulty

9.919583

Transactions

1

Size

201 B

Version

2

Bits

09eb69c5

Nonce

8,037

Timestamp

10/16/2013, 2:18:57 PM

Confirmations

6,614,210

Merkle Root

456283193792f14e760bfe67aca2836f834e5593fbd34177b6620c27472a0586
Transactions (1)
Coinbase456283193792f1…620c27472a0586
1 in β†’ 1 out10.1500 XPM110 B
AbuU1HhS…JPwsJEbB
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.

1.309 Γ— 10⁹⁷(98-digit number)
13098045088054743442…31003224165184807680
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
1.309 Γ— 10⁹⁷(98-digit number)
13098045088054743442…31003224165184807681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.619 Γ— 10⁹⁷(98-digit number)
26196090176109486885…62006448330369615361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.239 Γ— 10⁹⁷(98-digit number)
52392180352218973770…24012896660739230721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.047 Γ— 10⁹⁸(99-digit number)
10478436070443794754…48025793321478461441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.095 Γ— 10⁹⁸(99-digit number)
20956872140887589508…96051586642956922881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.191 Γ— 10⁹⁸(99-digit number)
41913744281775179016…92103173285913845761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.382 Γ— 10⁹⁸(99-digit number)
83827488563550358033…84206346571827691521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.676 Γ— 10⁹⁹(100-digit number)
16765497712710071606…68412693143655383041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.353 Γ— 10⁹⁹(100-digit number)
33530995425420143213…36825386287310766081
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 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
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 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 212914

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 1d4eb952c2631cae21ea29665c9f0dbde7de99f9111ae98e1f2ac6569e38fe8b

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 #212,914 on Chainz β†—
Circulating Supply:57,861,173 XPMΒ·at block #6,827,123 Β· updates every 60s
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