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Block #155,021

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2013, 1:34:17 AM Β· Difficulty 9.8651 Β· 6,641,608 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a1654ddb476916a57654edf25a8bcdff5ea3ab82fc53a27bb9e5b9ee74c53cab
View on Chainz β†—

Height

#155,021

Difficulty

9.865095

Transactions

1

Size

198 B

Version

2

Bits

09dd76e0

Nonce

430,073

Timestamp

9/8/2013, 1:34:17 AM

Confirmations

6,641,608

Merkle Root

8bffeafa15b479b5bc7eaca13b428944c54fec34ddba4812a2369c8752b83637
Transactions (1)
Coinbase8bffeafa15b479…369c8752b83637
1 in β†’ 1 out10.2600 XPM109 B
AJn9y9Wv…G4raUX4o
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.

1.726 Γ— 10⁹²(93-digit number)
17264512477893401108…97110639900871416000
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
1.726 Γ— 10⁹²(93-digit number)
17264512477893401108…97110639900871415999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.452 Γ— 10⁹²(93-digit number)
34529024955786802216…94221279801742831999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.905 Γ— 10⁹²(93-digit number)
69058049911573604433…88442559603485663999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.381 Γ— 10⁹³(94-digit number)
13811609982314720886…76885119206971327999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.762 Γ— 10⁹³(94-digit number)
27623219964629441773…53770238413942655999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.524 Γ— 10⁹³(94-digit number)
55246439929258883546…07540476827885311999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.104 Γ— 10⁹⁴(95-digit number)
11049287985851776709…15080953655770623999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.209 Γ— 10⁹⁴(95-digit number)
22098575971703553418…30161907311541247999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.419 Γ— 10⁹⁴(95-digit number)
44197151943407106837…60323814623082495999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.839 Γ— 10⁹⁴(95-digit number)
88394303886814213674…20647629246164991999
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 155021

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 a1654ddb476916a57654edf25a8bcdff5ea3ab82fc53a27bb9e5b9ee74c53cab

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 #155,021 on Chainz β†—
Circulating Supply:57,617,032 XPMΒ·at block #6,796,628 Β· updates every 60s
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