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Home/Chain Registry/Block #2,929,948

Block #2,929,948

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/19/2018, 11:33:20 AM Β· Difficulty 11.3894 Β· 3,910,114 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3237823e6250370024ffcccf241a60405380895423c8b3fdfe494ab49250fc05
View on Chainz β†—

Difficulty

11.389357

Transactions

1

Size

198 B

Version

2

Bits

0b63acea

Nonce

1,145,661,281

Timestamp

11/19/2018, 11:33:20 AM

Confirmations

3,910,114

Merkle Root

cd4a260fd6ade8073683273c478b7d73a595cd18202796fe42a6e9cbd0c0297b
Transactions (1)
Coinbasecd4a260fd6ade8…a6e9cbd0c0297b
1 in β†’ 1 out7.7000 XPM109 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.

3.474 Γ— 10⁹³(94-digit number)
34745456060831859735…92593853423746846080
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
3.474 Γ— 10⁹³(94-digit number)
34745456060831859735…92593853423746846079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.949 Γ— 10⁹³(94-digit number)
69490912121663719471…85187706847493692159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.389 Γ— 10⁹⁴(95-digit number)
13898182424332743894…70375413694987384319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.779 Γ— 10⁹⁴(95-digit number)
27796364848665487788…40750827389974768639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.559 Γ— 10⁹⁴(95-digit number)
55592729697330975577…81501654779949537279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.111 Γ— 10⁹⁡(96-digit number)
11118545939466195115…63003309559899074559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.223 Γ— 10⁹⁡(96-digit number)
22237091878932390230…26006619119798149119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.447 Γ— 10⁹⁡(96-digit number)
44474183757864780461…52013238239596298239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.894 Γ— 10⁹⁡(96-digit number)
88948367515729560923…04026476479192596479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.778 Γ— 10⁹⁢(97-digit number)
17789673503145912184…08052952958385192959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.557 Γ— 10⁹⁢(97-digit number)
35579347006291824369…16105905916770385919
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 2929948

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 3237823e6250370024ffcccf241a60405380895423c8b3fdfe494ab49250fc05

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 #2,929,948 on Chainz β†—
Circulating Supply:57,964,807 XPMΒ·at block #6,840,061 Β· updates every 60s
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