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Block #354,215

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/11/2014, 10:12:57 AM Β· Difficulty 10.3383 Β· 6,472,916 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ea822fc8ee2351676748b3676f7a806b0263aeba14c324ccb733a9630a6f1b16
View on Chainz β†—

Height

#354,215

Difficulty

10.338260

Transactions

1

Size

201 B

Version

2

Bits

0a569831

Nonce

43,879

Timestamp

1/11/2014, 10:12:57 AM

Confirmations

6,472,916

Merkle Root

086df8286f5bdcb47c03d5f55309c4837faf5edc443449806a76aa535647973d
Transactions (1)
Coinbase086df8286f5bdc…76aa535647973d
1 in β†’ 1 out9.3400 XPM111 B
ATczX4BZ…FQ1xfN7M
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.

2.230 Γ— 10⁹⁴(95-digit number)
22308604032048556995…64995885920777599040
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
2.230 Γ— 10⁹⁴(95-digit number)
22308604032048556995…64995885920777599041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.461 Γ— 10⁹⁴(95-digit number)
44617208064097113991…29991771841555198081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.923 Γ— 10⁹⁴(95-digit number)
89234416128194227983…59983543683110396161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.784 Γ— 10⁹⁡(96-digit number)
17846883225638845596…19967087366220792321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.569 Γ— 10⁹⁡(96-digit number)
35693766451277691193…39934174732441584641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.138 Γ— 10⁹⁡(96-digit number)
71387532902555382386…79868349464883169281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.427 Γ— 10⁹⁢(97-digit number)
14277506580511076477…59736698929766338561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.855 Γ— 10⁹⁢(97-digit number)
28555013161022152954…19473397859532677121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.711 Γ— 10⁹⁢(97-digit number)
57110026322044305909…38946795719065354241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.142 Γ— 10⁹⁷(98-digit number)
11422005264408861181…77893591438130708481
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 354215

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 ea822fc8ee2351676748b3676f7a806b0263aeba14c324ccb733a9630a6f1b16

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 #354,215 on Chainz β†—
Circulating Supply:57,861,228 XPMΒ·at block #6,827,130 Β· updates every 60s
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