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Block #341,243

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/3/2014, 8:14:13 AM Β· Difficulty 10.1343 Β· 6,463,642 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2b5e9300eee706a6bb25caad9d16b0c83b103bf6a3704d4f4e3cbeb0c003b6e2
View on Chainz β†—

Height

#341,243

Difficulty

10.134336

Transactions

1

Size

207 B

Version

2

Bits

0a2263d9

Nonce

318,768,859

Timestamp

1/3/2014, 8:14:13 AM

Confirmations

6,463,642

Merkle Root

7089ce66be24bae8ca2ea8826ab60bab13a5819fd6d8c95519ea38db9874efb3
Transactions (1)
Coinbase7089ce66be24ba…ea38db9874efb3
1 in β†’ 1 out9.7200 XPM116 B
AbwWkWZt…kawDhufa
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.

7.585 Γ— 10⁹⁢(97-digit number)
75852603375684547213…86848354195050891520
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
7.585 Γ— 10⁹⁢(97-digit number)
75852603375684547213…86848354195050891519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.517 Γ— 10⁹⁷(98-digit number)
15170520675136909442…73696708390101783039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.034 Γ— 10⁹⁷(98-digit number)
30341041350273818885…47393416780203566079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.068 Γ— 10⁹⁷(98-digit number)
60682082700547637770…94786833560407132159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.213 Γ— 10⁹⁸(99-digit number)
12136416540109527554…89573667120814264319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.427 Γ— 10⁹⁸(99-digit number)
24272833080219055108…79147334241628528639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.854 Γ— 10⁹⁸(99-digit number)
48545666160438110216…58294668483257057279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.709 Γ— 10⁹⁸(99-digit number)
97091332320876220433…16589336966514114559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.941 Γ— 10⁹⁹(100-digit number)
19418266464175244086…33178673933028229119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.883 Γ— 10⁹⁹(100-digit number)
38836532928350488173…66357347866056458239
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 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
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 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 341243

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 2b5e9300eee706a6bb25caad9d16b0c83b103bf6a3704d4f4e3cbeb0c003b6e2

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 #341,243 on Chainz β†—
Circulating Supply:57,683,157 XPMΒ·at block #6,804,884 Β· updates every 60s
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