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Block #221,581

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/21/2013, 3:52:01 PM Β· Difficulty 9.9393 Β· 6,579,122 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e1f76319d9736d9e15d7f2f0e3010bcd4b2f1e635742eab6fb2ed1bd8529c81
View on Chainz β†—

Height

#221,581

Difficulty

9.939288

Transactions

1

Size

208 B

Version

2

Bits

09f0752b

Nonce

33,559,068

Timestamp

10/21/2013, 3:52:01 PM

Confirmations

6,579,122

Merkle Root

a8f1ed785d55b5e39983ef713f9d08ac2f0bbd32b8d4aef5894ff43860563d47
Transactions (1)
Coinbasea8f1ed785d55b5…4ff43860563d47
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.762 Γ— 10¹⁰⁰(101-digit number)
17629150535435668609…55046231114109690720
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
1.762 Γ— 10¹⁰⁰(101-digit number)
17629150535435668609…55046231114109690719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.525 Γ— 10¹⁰⁰(101-digit number)
35258301070871337219…10092462228219381439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.051 Γ— 10¹⁰⁰(101-digit number)
70516602141742674438…20184924456438762879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.410 Γ— 10¹⁰¹(102-digit number)
14103320428348534887…40369848912877525759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.820 Γ— 10¹⁰¹(102-digit number)
28206640856697069775…80739697825755051519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.641 Γ— 10¹⁰¹(102-digit number)
56413281713394139551…61479395651510103039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.128 Γ— 10¹⁰²(103-digit number)
11282656342678827910…22958791303020206079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.256 Γ— 10¹⁰²(103-digit number)
22565312685357655820…45917582606040412159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.513 Γ— 10¹⁰²(103-digit number)
45130625370715311640…91835165212080824319
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 221581

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 4e1f76319d9736d9e15d7f2f0e3010bcd4b2f1e635742eab6fb2ed1bd8529c81

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 #221,581 on Chainz β†—
Circulating Supply:57,649,690 XPMΒ·at block #6,800,702 Β· updates every 60s
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