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Block #178,628

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/24/2013, 1:03:55 PM Β· Difficulty 9.8630 Β· 6,623,072 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c387a5fa4e47b779861ff72e356323779d9f3d4f1e0d86ffe8faedf8f799e7a3
View on Chainz β†—

Height

#178,628

Difficulty

9.862952

Transactions

1

Size

199 B

Version

2

Bits

09dcea6e

Nonce

35,075

Timestamp

9/24/2013, 1:03:55 PM

Confirmations

6,623,072

Merkle Root

5161799bfb8718d665b40941fbfcb93e2021e7157d4b33991ae18bf39688636d
Transactions (1)
Coinbase5161799bfb8718…e18bf39688636d
1 in β†’ 1 out10.2600 XPM109 B
ATK4r8Gh…Usic4A9N
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.

4.094 Γ— 10⁹⁴(95-digit number)
40944786752985111956…04696955887898949100
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
4.094 Γ— 10⁹⁴(95-digit number)
40944786752985111956…04696955887898949099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.188 Γ— 10⁹⁴(95-digit number)
81889573505970223912…09393911775797898199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.637 Γ— 10⁹⁡(96-digit number)
16377914701194044782…18787823551595796399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.275 Γ— 10⁹⁡(96-digit number)
32755829402388089565…37575647103191592799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.551 Γ— 10⁹⁡(96-digit number)
65511658804776179130…75151294206383185599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.310 Γ— 10⁹⁢(97-digit number)
13102331760955235826…50302588412766371199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.620 Γ— 10⁹⁢(97-digit number)
26204663521910471652…00605176825532742399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.240 Γ— 10⁹⁢(97-digit number)
52409327043820943304…01210353651065484799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.048 Γ— 10⁹⁷(98-digit number)
10481865408764188660…02420707302130969599
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 178628

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 c387a5fa4e47b779861ff72e356323779d9f3d4f1e0d86ffe8faedf8f799e7a3

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 #178,628 on Chainz β†—
Circulating Supply:57,657,690 XPMΒ·at block #6,801,699 Β· updates every 60s
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