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Block #113,478

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/12/2013, 1:48:31 PM Β· Difficulty 9.7326 Β· 6,681,865 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fb30fe2f4d2409ed7d7c65524f36df2c0b634fd2dcc34aded8f93d21252b5515
View on Chainz β†—

Height

#113,478

Difficulty

9.732556

Transactions

1

Size

200 B

Version

2

Bits

09bb88c5

Nonce

4,931

Timestamp

8/12/2013, 1:48:31 PM

Confirmations

6,681,865

Merkle Root

eb0c41cc25cc4a59550c017a836bbb2d994ecad38e6360b4d593899837325e20
Transactions (1)
Coinbaseeb0c41cc25cc4a…93899837325e20
1 in β†’ 1 out10.5400 XPM109 B
AZxbBNyf…fG5TfXgf
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.

1.494 Γ— 10⁹⁢(97-digit number)
14945935400442793543…28218311462503503920
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
1.494 Γ— 10⁹⁢(97-digit number)
14945935400442793543…28218311462503503919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.989 Γ— 10⁹⁢(97-digit number)
29891870800885587087…56436622925007007839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.978 Γ— 10⁹⁢(97-digit number)
59783741601771174174…12873245850014015679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.195 Γ— 10⁹⁷(98-digit number)
11956748320354234834…25746491700028031359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.391 Γ— 10⁹⁷(98-digit number)
23913496640708469669…51492983400056062719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.782 Γ— 10⁹⁷(98-digit number)
47826993281416939339…02985966800112125439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.565 Γ— 10⁹⁷(98-digit number)
95653986562833878679…05971933600224250879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.913 Γ— 10⁹⁸(99-digit number)
19130797312566775735…11943867200448501759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.826 Γ— 10⁹⁸(99-digit number)
38261594625133551471…23887734400897003519
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 113478

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 fb30fe2f4d2409ed7d7c65524f36df2c0b634fd2dcc34aded8f93d21252b5515

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 #113,478 on Chainz β†—
Circulating Supply:57,606,796 XPMΒ·at block #6,795,342 Β· updates every 60s
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