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Home/Chain Registry/Block #2,640,247

Block #2,640,247

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 10:35:29 PM Β· Difficulty 11.5733 Β· 4,202,800 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4597376ed75193d5e11975aad6396fa336b9fd07081e503412bc8f8b4f7fe1b0
View on Chainz β†—

Difficulty

11.573267

Transactions

1

Size

199 B

Version

2

Bits

0b92c1a2

Nonce

706,053,576

Timestamp

4/30/2018, 10:35:29 PM

Confirmations

4,202,800

Merkle Root

077b2574515d258e52b5bfa872553bda7cb8e21a64a0bc827fcb0e28667699d2
Transactions (1)
Coinbase077b2574515d25…cb0e28667699d2
1 in β†’ 1 out7.4500 XPM110 B
Abs6xztv…ysnShdK3
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.

3.050 Γ— 10⁹²(93-digit number)
30506719965820678458…63195348887283802880
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
3.050 Γ— 10⁹²(93-digit number)
30506719965820678458…63195348887283802879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.101 Γ— 10⁹²(93-digit number)
61013439931641356916…26390697774567605759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.220 Γ— 10⁹³(94-digit number)
12202687986328271383…52781395549135211519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.440 Γ— 10⁹³(94-digit number)
24405375972656542766…05562791098270423039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.881 Γ— 10⁹³(94-digit number)
48810751945313085533…11125582196540846079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.762 Γ— 10⁹³(94-digit number)
97621503890626171067…22251164393081692159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.952 Γ— 10⁹⁴(95-digit number)
19524300778125234213…44502328786163384319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.904 Γ— 10⁹⁴(95-digit number)
39048601556250468426…89004657572326768639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.809 Γ— 10⁹⁴(95-digit number)
78097203112500936853…78009315144653537279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.561 Γ— 10⁹⁡(96-digit number)
15619440622500187370…56018630289307074559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.123 Γ— 10⁹⁡(96-digit number)
31238881245000374741…12037260578614149119
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 2640247

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 4597376ed75193d5e11975aad6396fa336b9fd07081e503412bc8f8b4f7fe1b0

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 #2,640,247 on Chainz β†—
Circulating Supply:57,988,733 XPMΒ·at block #6,843,046 Β· updates every 60s
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