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Home/Chain Registry/Block #120,931

Block #120,931

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/17/2013, 11:59:27 AM Β· Difficulty 9.7516 Β· 6,715,632 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
69181c285641295907c68593aaa1d637ce277ae5f95f717dea10ff109172a44b
View on Chainz β†—

Height

#120,931

Difficulty

9.751579

Transactions

1

Size

200 B

Version

2

Bits

09c06779

Nonce

10,422

Timestamp

8/17/2013, 11:59:27 AM

Confirmations

6,715,632

Merkle Root

dc3dd6b92bc02c560c34530a39daa067f95f6e8f04db0f46aac768f725d13607
Transactions (1)
Coinbasedc3dd6b92bc02c…c768f725d13607
1 in β†’ 1 out10.5000 XPM109 B
AHmvhRqW…qgG5FwBR
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.

2.395 Γ— 10⁹⁸(99-digit number)
23957683709675322380…74732720618577378850
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
2.395 Γ— 10⁹⁸(99-digit number)
23957683709675322380…74732720618577378849
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.791 Γ— 10⁹⁸(99-digit number)
47915367419350644760…49465441237154757699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.583 Γ— 10⁹⁸(99-digit number)
95830734838701289521…98930882474309515399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.916 Γ— 10⁹⁹(100-digit number)
19166146967740257904…97861764948619030799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.833 Γ— 10⁹⁹(100-digit number)
38332293935480515808…95723529897238061599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.666 Γ— 10⁹⁹(100-digit number)
76664587870961031616…91447059794476123199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.533 Γ— 10¹⁰⁰(101-digit number)
15332917574192206323…82894119588952246399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.066 Γ— 10¹⁰⁰(101-digit number)
30665835148384412646…65788239177904492799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.133 Γ— 10¹⁰⁰(101-digit number)
61331670296768825293…31576478355808985599
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 120931

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 69181c285641295907c68593aaa1d637ce277ae5f95f717dea10ff109172a44b

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 #120,931 on Chainz β†—
Circulating Supply:57,936,771 XPMΒ·at block #6,836,562 Β· updates every 60s
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