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Block #121,082

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/17/2013, 2:23:13 PM Β· Difficulty 9.7520 Β· 6,704,625 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
53acb9910e53f102a81497762d139b381ebf4c559807899db897eb820be030a1
View on Chainz β†—

Height

#121,082

Difficulty

9.751981

Transactions

1

Size

201 B

Version

2

Bits

09c081d7

Nonce

307,782

Timestamp

8/17/2013, 2:23:13 PM

Confirmations

6,704,625

Merkle Root

6596c1c4a939f4a1794b1c3f48aae7e7014d070327b98d9bb13502329cadb645
Transactions (1)
Coinbase6596c1c4a939f4…3502329cadb645
1 in β†’ 1 out10.5000 XPM109 B
AKaGDwVV…h5Bk5GFu
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.

2.900 Γ— 10⁹⁹(100-digit number)
29001293233973396399…63547448200271526080
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
2.900 Γ— 10⁹⁹(100-digit number)
29001293233973396399…63547448200271526079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.800 Γ— 10⁹⁹(100-digit number)
58002586467946792798…27094896400543052159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.160 Γ— 10¹⁰⁰(101-digit number)
11600517293589358559…54189792801086104319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.320 Γ— 10¹⁰⁰(101-digit number)
23201034587178717119…08379585602172208639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.640 Γ— 10¹⁰⁰(101-digit number)
46402069174357434238…16759171204344417279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.280 Γ— 10¹⁰⁰(101-digit number)
92804138348714868477…33518342408688834559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.856 Γ— 10¹⁰¹(102-digit number)
18560827669742973695…67036684817377669119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.712 Γ— 10¹⁰¹(102-digit number)
37121655339485947391…34073369634755338239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.424 Γ— 10¹⁰¹(102-digit number)
74243310678971894782…68146739269510676479
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 121082

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 53acb9910e53f102a81497762d139b381ebf4c559807899db897eb820be030a1

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 #121,082 on Chainz β†—
Circulating Supply:57,849,760 XPMΒ·at block #6,825,706 Β· updates every 60s
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