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Block #580,514

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/7/2014, 8:45:02 PM Β· Difficulty 10.9649 Β· 6,221,203 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
906efccb2370d5bc413a8d4e558df68ddd2d1673eaab5a85ef1fe9e218393328
View on Chainz β†—

Height

#580,514

Difficulty

10.964875

Transactions

1

Size

244 B

Version

2

Bits

0af70206

Nonce

2,370,763

Timestamp

6/7/2014, 8:45:02 PM

Confirmations

6,221,203

Merkle Root

342b57080fd04e38983e60fcf4b2eb92281069110b5e0c1aef060c5da82ab3c8
Transactions (1)
Coinbase342b57080fd04e…060c5da82ab3c8
1 in β†’ 2 out8.3000 XPM152 B
AXn1KW6P…c7VDu2zvALPu3s2c…EJXLjVFh
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.

6.843 Γ— 10⁹⁹(100-digit number)
68437134435877297428…57757799856659312640
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
6.843 Γ— 10⁹⁹(100-digit number)
68437134435877297428…57757799856659312639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.368 Γ— 10¹⁰⁰(101-digit number)
13687426887175459485…15515599713318625279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.737 Γ— 10¹⁰⁰(101-digit number)
27374853774350918971…31031199426637250559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.474 Γ— 10¹⁰⁰(101-digit number)
54749707548701837942…62062398853274501119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.094 Γ— 10¹⁰¹(102-digit number)
10949941509740367588…24124797706549002239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.189 Γ— 10¹⁰¹(102-digit number)
21899883019480735177…48249595413098004479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.379 Γ— 10¹⁰¹(102-digit number)
43799766038961470354…96499190826196008959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.759 Γ— 10¹⁰¹(102-digit number)
87599532077922940708…92998381652392017919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.751 Γ— 10¹⁰²(103-digit number)
17519906415584588141…85996763304784035839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.503 Γ— 10¹⁰²(103-digit number)
35039812831169176283…71993526609568071679
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 580514

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 906efccb2370d5bc413a8d4e558df68ddd2d1673eaab5a85ef1fe9e218393328

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 #580,514 on Chainz β†—
Circulating Supply:57,657,821 XPMΒ·at block #6,801,716 Β· updates every 60s
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