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Block #113,542

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/12/2013, 2:44:38 PM Β· Difficulty 9.7331 Β· 6,681,402 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
115184dccce78e992304754056efca0090d0c240b3dba8286ec861eeff2ee161
View on Chainz β†—

Height

#113,542

Difficulty

9.733063

Transactions

1

Size

198 B

Version

2

Bits

09bbaa08

Nonce

458,277

Timestamp

8/12/2013, 2:44:38 PM

Confirmations

6,681,402

Merkle Root

7393dbdf30355246c7d20f7988a5d24648f5504a63129f82111691c67ed94280
Transactions (1)
Coinbase7393dbdf303552…1691c67ed94280
1 in β†’ 1 out10.5400 XPM109 B
Ac7axLu9…iYGbqsAx
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.

7.832 Γ— 10⁹¹(92-digit number)
78328280985361953156…73668984873913940400
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
7.832 Γ— 10⁹¹(92-digit number)
78328280985361953156…73668984873913940399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.566 Γ— 10⁹²(93-digit number)
15665656197072390631…47337969747827880799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.133 Γ— 10⁹²(93-digit number)
31331312394144781262…94675939495655761599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.266 Γ— 10⁹²(93-digit number)
62662624788289562525…89351878991311523199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.253 Γ— 10⁹³(94-digit number)
12532524957657912505…78703757982623046399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.506 Γ— 10⁹³(94-digit number)
25065049915315825010…57407515965246092799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.013 Γ— 10⁹³(94-digit number)
50130099830631650020…14815031930492185599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.002 Γ— 10⁹⁴(95-digit number)
10026019966126330004…29630063860984371199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.005 Γ— 10⁹⁴(95-digit number)
20052039932252660008…59260127721968742399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.010 Γ— 10⁹⁴(95-digit number)
40104079864505320016…18520255443937484799
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 113542

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 115184dccce78e992304754056efca0090d0c240b3dba8286ec861eeff2ee161

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 #113,542 on Chainz β†—
Circulating Supply:57,603,587 XPMΒ·at block #6,794,943 Β· updates every 60s
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