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Block #132,820

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/25/2013, 3:58:23 AM Β· Difficulty 9.7908 Β· 6,681,192 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0c3e65599756c8a87bad005edc1b3d03fb80fc8c199a541cef2b830ae6c2029b
View on Chainz β†—

Height

#132,820

Difficulty

9.790812

Transactions

1

Size

201 B

Version

2

Bits

09ca72a4

Nonce

2,320,703

Timestamp

8/25/2013, 3:58:23 AM

Confirmations

6,681,192

Merkle Root

ad0f9061c7831acac5c2377c00e52098b27eb7a3a2f7bb8d2e87209b02698b3a
Transactions (1)
Coinbasead0f9061c7831a…87209b02698b3a
1 in β†’ 1 out10.4200 XPM109 B
AY88KHST…88L8yacq
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.

1.078 Γ— 10¹⁰⁰(101-digit number)
10787861698215331950…54649525429872787740
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
1.078 Γ— 10¹⁰⁰(101-digit number)
10787861698215331950…54649525429872787739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.157 Γ— 10¹⁰⁰(101-digit number)
21575723396430663901…09299050859745575479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.315 Γ— 10¹⁰⁰(101-digit number)
43151446792861327802…18598101719491150959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.630 Γ— 10¹⁰⁰(101-digit number)
86302893585722655605…37196203438982301919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.726 Γ— 10¹⁰¹(102-digit number)
17260578717144531121…74392406877964603839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.452 Γ— 10¹⁰¹(102-digit number)
34521157434289062242…48784813755929207679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.904 Γ— 10¹⁰¹(102-digit number)
69042314868578124484…97569627511858415359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.380 Γ— 10¹⁰²(103-digit number)
13808462973715624896…95139255023716830719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.761 Γ— 10¹⁰²(103-digit number)
27616925947431249793…90278510047433661439
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 132820

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 0c3e65599756c8a87bad005edc1b3d03fb80fc8c199a541cef2b830ae6c2029b

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 #132,820 on Chainz β†—
Circulating Supply:57,756,179 XPMΒ·at block #6,814,011 Β· updates every 60s
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