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Home/Chain Registry/Block #2,929,946

Block #2,929,946

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/19/2018, 11:31:39 AM Β· Difficulty 11.3892 Β· 3,909,971 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cc29ec0f9294833e013f1d1409e395544d96a1f044d758f5236efdc867d8140f
View on Chainz β†—

Difficulty

11.389224

Transactions

1

Size

201 B

Version

2

Bits

0b63a42d

Nonce

1,607,079,957

Timestamp

11/19/2018, 11:31:39 AM

Confirmations

3,909,971

Merkle Root

d3711f5d39beaf7f66927d9f15f44528bb1cb2d95e3ef97bbee259eb8985252c
Transactions (1)
Coinbased3711f5d39beaf…e259eb8985252c
1 in β†’ 1 out7.7000 XPM110 B
AbXwmGxD…4XXYP765
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.

1.462 Γ— 10⁹⁢(97-digit number)
14620041670345945155…23262074160999475200
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
1.462 Γ— 10⁹⁢(97-digit number)
14620041670345945155…23262074160999475199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.924 Γ— 10⁹⁢(97-digit number)
29240083340691890311…46524148321998950399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.848 Γ— 10⁹⁢(97-digit number)
58480166681383780622…93048296643997900799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.169 Γ— 10⁹⁷(98-digit number)
11696033336276756124…86096593287995801599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.339 Γ— 10⁹⁷(98-digit number)
23392066672553512249…72193186575991603199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.678 Γ— 10⁹⁷(98-digit number)
46784133345107024498…44386373151983206399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.356 Γ— 10⁹⁷(98-digit number)
93568266690214048996…88772746303966412799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.871 Γ— 10⁹⁸(99-digit number)
18713653338042809799…77545492607932825599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.742 Γ— 10⁹⁸(99-digit number)
37427306676085619598…55090985215865651199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.485 Γ— 10⁹⁸(99-digit number)
74854613352171239196…10181970431731302399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.497 Γ— 10⁹⁹(100-digit number)
14970922670434247839…20363940863462604799
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 2929946

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 cc29ec0f9294833e013f1d1409e395544d96a1f044d758f5236efdc867d8140f

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 #2,929,946 on Chainz β†—
Circulating Supply:57,963,637 XPMΒ·at block #6,839,916 Β· updates every 60s
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