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Block #612,269

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/2/2014, 2:08:28 PM Β· Difficulty 10.9260 Β· 6,199,465 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8ea0b8d768d61fe370fdf7f84d598be5715050957723eeddf0e5f1ebca38ecab
View on Chainz β†—

Height

#612,269

Difficulty

10.926007

Transactions

2

Size

1.87 KB

Version

2

Bits

0aed0ec5

Nonce

1,149,823,310

Timestamp

7/2/2014, 2:08:28 PM

Confirmations

6,199,465

Merkle Root

64c46076b6569ebb3c9a3bf63040afbd4c2dcc7f37dc41bd3ab018de73defed3
Transactions (2)
Coinbasef1e488613de114…8f0e0f36c16a8f
1 in β†’ 1 out8.3800 XPM116 B
ANSXnLY2…Sd25TjkD
36964bf7870bc7…7028b9d9ea0ce2
11 in β†’ 2 out45.0288 XPM1.66 KB
AVueCtUb…xurC6eVqAMEoXpq5…yCJBX6A3
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.

6.042 Γ— 10⁹⁷(98-digit number)
60421761535556354591…05807913563403679200
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
6.042 Γ— 10⁹⁷(98-digit number)
60421761535556354591…05807913563403679199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.208 Γ— 10⁹⁸(99-digit number)
12084352307111270918…11615827126807358399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.416 Γ— 10⁹⁸(99-digit number)
24168704614222541836…23231654253614716799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.833 Γ— 10⁹⁸(99-digit number)
48337409228445083673…46463308507229433599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.667 Γ— 10⁹⁸(99-digit number)
96674818456890167346…92926617014458867199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.933 Γ— 10⁹⁹(100-digit number)
19334963691378033469…85853234028917734399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.866 Γ— 10⁹⁹(100-digit number)
38669927382756066938…71706468057835468799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.733 Γ— 10⁹⁹(100-digit number)
77339854765512133876…43412936115670937599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.546 Γ— 10¹⁰⁰(101-digit number)
15467970953102426775…86825872231341875199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.093 Γ— 10¹⁰⁰(101-digit number)
30935941906204853550…73651744462683750399
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 612269

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 8ea0b8d768d61fe370fdf7f84d598be5715050957723eeddf0e5f1ebca38ecab

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 #612,269 on Chainz β†—
Circulating Supply:57,737,980 XPMΒ·at block #6,811,733 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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