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Home/Chain Registry/Block #2,639,024

Block #2,639,024

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 12:17:03 PM Β· Difficulty 11.5188 Β· 4,197,986 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
597e8506675c5fa828190a6eb4ef2809e2e40c0d59bca2c8d5f052f68042d96b
View on Chainz β†—

Difficulty

11.518848

Transactions

1

Size

199 B

Version

2

Bits

0b84d33a

Nonce

880,606,230

Timestamp

4/30/2018, 12:17:03 PM

Confirmations

4,197,986

Merkle Root

b76927674eb0f9158e0936c94201e2339d1519b0c27fe7b4587b96d5cc860848
Transactions (1)
Coinbaseb76927674eb0f9…7b96d5cc860848
1 in β†’ 1 out7.5200 XPM109 B
AdhYDCUp…XEfK2MXR
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.

3.118 Γ— 10⁹⁡(96-digit number)
31185133591081685786…94889174461518460560
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
3.118 Γ— 10⁹⁡(96-digit number)
31185133591081685786…94889174461518460559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.237 Γ— 10⁹⁡(96-digit number)
62370267182163371572…89778348923036921119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.247 Γ— 10⁹⁢(97-digit number)
12474053436432674314…79556697846073842239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.494 Γ— 10⁹⁢(97-digit number)
24948106872865348629…59113395692147684479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.989 Γ— 10⁹⁢(97-digit number)
49896213745730697258…18226791384295368959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.979 Γ— 10⁹⁢(97-digit number)
99792427491461394516…36453582768590737919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.995 Γ— 10⁹⁷(98-digit number)
19958485498292278903…72907165537181475839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.991 Γ— 10⁹⁷(98-digit number)
39916970996584557806…45814331074362951679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.983 Γ— 10⁹⁷(98-digit number)
79833941993169115612…91628662148725903359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.596 Γ— 10⁹⁸(99-digit number)
15966788398633823122…83257324297451806719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.193 Γ— 10⁹⁸(99-digit number)
31933576797267646245…66514648594903613439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2639024

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 597e8506675c5fa828190a6eb4ef2809e2e40c0d59bca2c8d5f052f68042d96b

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 #2,639,024 on Chainz β†—
Circulating Supply:57,940,376 XPMΒ·at block #6,837,009 Β· updates every 60s
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