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Block #340,363

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/2/2014, 5:53:19 PM Β· Difficulty 10.1309 Β· 6,486,019 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f9ff20c68a86b5f5fc7c0c139056d64baf74365cc860ad7b10ba3fbc7e656504
View on Chainz β†—

Height

#340,363

Difficulty

10.130892

Transactions

1

Size

210 B

Version

2

Bits

0a21822b

Nonce

22,604

Timestamp

1/2/2014, 5:53:19 PM

Confirmations

6,486,019

Merkle Root

305dec4070d2d35afd31c5f693a48e2edc3eb44a64c04ac1256bc86b41648471
Transactions (1)
Coinbase305dec4070d2d3…6bc86b41648471
1 in β†’ 1 out9.7300 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.

2.727 Γ— 10¹⁰⁴(105-digit number)
27271119637992137860…63407614335638348280
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
2.727 Γ— 10¹⁰⁴(105-digit number)
27271119637992137860…63407614335638348279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.454 Γ— 10¹⁰⁴(105-digit number)
54542239275984275721…26815228671276696559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.090 Γ— 10¹⁰⁡(106-digit number)
10908447855196855144…53630457342553393119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.181 Γ— 10¹⁰⁡(106-digit number)
21816895710393710288…07260914685106786239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.363 Γ— 10¹⁰⁡(106-digit number)
43633791420787420577…14521829370213572479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.726 Γ— 10¹⁰⁡(106-digit number)
87267582841574841154…29043658740427144959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.745 Γ— 10¹⁰⁢(107-digit number)
17453516568314968230…58087317480854289919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.490 Γ— 10¹⁰⁢(107-digit number)
34907033136629936461…16174634961708579839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.981 Γ— 10¹⁰⁢(107-digit number)
69814066273259872923…32349269923417159679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.396 Γ— 10¹⁰⁷(108-digit number)
13962813254651974584…64698539846834319359
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 340363

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 f9ff20c68a86b5f5fc7c0c139056d64baf74365cc860ad7b10ba3fbc7e656504

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 #340,363 on Chainz β†—
Circulating Supply:57,855,202 XPMΒ·at block #6,826,381 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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