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Block #529,639

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 5/7/2014, 9:10:39 AM Β· Difficulty 10.8904 Β· 6,295,329 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
149291e6e53fa9fa5883b5abe64912add2eb0bcfb2f628bf637fea2522f0bccc
View on Chainz β†—

Height

#529,639

Difficulty

10.890380

Transactions

1

Size

209 B

Version

2

Bits

0ae3eff0

Nonce

176,121,334

Timestamp

5/7/2014, 9:10:39 AM

Confirmations

6,295,329

Merkle Root

dc6e9a448f7542647926b65230f926641419f7df099f823c985646e00c4d9424
Transactions (1)
Coinbasedc6e9a448f7542…5646e00c4d9424
1 in β†’ 1 out8.4200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

6.979 Γ— 10¹⁰⁰(101-digit number)
69794829100903434165…98017890335756672000
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
6.979 Γ— 10¹⁰⁰(101-digit number)
69794829100903434165…98017890335756671999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.395 Γ— 10¹⁰¹(102-digit number)
13958965820180686833…96035780671513343999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.791 Γ— 10¹⁰¹(102-digit number)
27917931640361373666…92071561343026687999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.583 Γ— 10¹⁰¹(102-digit number)
55835863280722747332…84143122686053375999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.116 Γ— 10¹⁰²(103-digit number)
11167172656144549466…68286245372106751999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.233 Γ— 10¹⁰²(103-digit number)
22334345312289098933…36572490744213503999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.466 Γ— 10¹⁰²(103-digit number)
44668690624578197866…73144981488427007999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.933 Γ— 10¹⁰²(103-digit number)
89337381249156395732…46289962976854015999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.786 Γ— 10¹⁰³(104-digit number)
17867476249831279146…92579925953708031999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.573 Γ— 10¹⁰³(104-digit number)
35734952499662558292…85159851907416063999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.146 Γ— 10¹⁰³(104-digit number)
71469904999325116585…70319703814832127999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.429 Γ— 10¹⁰⁴(105-digit number)
14293980999865023317…40639407629664255999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 529639

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 149291e6e53fa9fa5883b5abe64912add2eb0bcfb2f628bf637fea2522f0bccc

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 #529,639 on Chainz β†—
Circulating Supply:57,843,825 XPMΒ·at block #6,824,967 Β· updates every 60s
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