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Home/Chain Registry/Block #2,645,584

Block #2,645,584

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 11:35:19 PM Β· Difficulty 11.7349 Β· 4,196,994 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e6aa752fb4fcd0a06a56adc9cc842c26489b298e3695dd55eec1cf953edf7a55
View on Chainz β†—

Difficulty

11.734934

Transactions

1

Size

200 B

Version

2

Bits

0bbc24aa

Nonce

432,913,245

Timestamp

5/2/2018, 11:35:19 PM

Confirmations

4,196,994

Merkle Root

cac699a0bf67a3b0be4a471788d2fa3a204a421b7382b439e4d37cb2b19f4b63
Transactions (1)
Coinbasecac699a0bf67a3…d37cb2b19f4b63
1 in β†’ 1 out7.2500 XPM109 B
ASBDQ7zs…z3i2hb6h
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.

4.350 Γ— 10⁹⁢(97-digit number)
43504609563842094203…45254780032490864640
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
4.350 Γ— 10⁹⁢(97-digit number)
43504609563842094203…45254780032490864639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.700 Γ— 10⁹⁢(97-digit number)
87009219127684188407…90509560064981729279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.740 Γ— 10⁹⁷(98-digit number)
17401843825536837681…81019120129963458559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.480 Γ— 10⁹⁷(98-digit number)
34803687651073675363…62038240259926917119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.960 Γ— 10⁹⁷(98-digit number)
69607375302147350726…24076480519853834239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.392 Γ— 10⁹⁸(99-digit number)
13921475060429470145…48152961039707668479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.784 Γ— 10⁹⁸(99-digit number)
27842950120858940290…96305922079415336959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.568 Γ— 10⁹⁸(99-digit number)
55685900241717880581…92611844158830673919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.113 Γ— 10⁹⁹(100-digit number)
11137180048343576116…85223688317661347839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.227 Γ— 10⁹⁹(100-digit number)
22274360096687152232…70447376635322695679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.454 Γ— 10⁹⁹(100-digit number)
44548720193374304464…40894753270645391359
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 2645584

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 e6aa752fb4fcd0a06a56adc9cc842c26489b298e3695dd55eec1cf953edf7a55

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 #2,645,584 on Chainz β†—
Circulating Supply:57,985,052 XPMΒ·at block #6,842,577 Β· updates every 60s
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