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Home/Chain Registry/Block #2,644,935

Block #2,644,935

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 4:57:31 PM Β· Difficulty 11.7214 Β· 4,188,979 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ca02c9edaa675ab979be366a663c522c70c9ead99a286bd7dda2a37a2a1ac6c9
View on Chainz β†—

Difficulty

11.721371

Transactions

1

Size

201 B

Version

2

Bits

0bb8abc0

Nonce

1,141,721,330

Timestamp

5/2/2018, 4:57:31 PM

Confirmations

4,188,979

Merkle Root

eb5334e3dcfc5dbad836bdfc8ec36f09b291137e7f59ac3d1c92a1486dba4a25
Transactions (1)
Coinbaseeb5334e3dcfc5d…92a1486dba4a25
1 in β†’ 1 out7.2700 XPM110 B
ALoWtYFL…i9PW3ewA
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.

9.737 Γ— 10⁹⁢(97-digit number)
97378320966391959781…44364905579585953280
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
9.737 Γ— 10⁹⁢(97-digit number)
97378320966391959781…44364905579585953279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.947 Γ— 10⁹⁷(98-digit number)
19475664193278391956…88729811159171906559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.895 Γ— 10⁹⁷(98-digit number)
38951328386556783912…77459622318343813119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.790 Γ— 10⁹⁷(98-digit number)
77902656773113567824…54919244636687626239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.558 Γ— 10⁹⁸(99-digit number)
15580531354622713564…09838489273375252479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.116 Γ— 10⁹⁸(99-digit number)
31161062709245427129…19676978546750504959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.232 Γ— 10⁹⁸(99-digit number)
62322125418490854259…39353957093501009919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.246 Γ— 10⁹⁹(100-digit number)
12464425083698170851…78707914187002019839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.492 Γ— 10⁹⁹(100-digit number)
24928850167396341703…57415828374004039679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.985 Γ— 10⁹⁹(100-digit number)
49857700334792683407…14831656748008079359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.971 Γ— 10⁹⁹(100-digit number)
99715400669585366815…29663313496016158719
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 2644935

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 ca02c9edaa675ab979be366a663c522c70c9ead99a286bd7dda2a37a2a1ac6c9

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 #2,644,935 on Chainz β†—
Circulating Supply:57,915,538 XPMΒ·at block #6,833,913 Β· updates every 60s
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