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Home/Chain Registry/Block #2,144,271

Block #2,144,271

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/3/2017, 10:19:00 PM Β· Difficulty 10.8841 Β· 4,698,610 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e84cac958c0b820573820c2abe5e638c64b94fe1c5a74ef6b84d71ddaf3cabb
View on Chainz β†—

Difficulty

10.884054

Transactions

1

Size

200 B

Version

2

Bits

0ae25164

Nonce

67,146,274

Timestamp

6/3/2017, 10:19:00 PM

Confirmations

4,698,610

Merkle Root

83fe6d702dfa6d377da9179ae666986b7ae14c5b0beb3ccab6e111f6af2ed657
Transactions (1)
Coinbase83fe6d702dfa6d…e111f6af2ed657
1 in β†’ 1 out8.4300 XPM110 B
APK1fQD1…Xshg7XM6
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.

2.576 Γ— 10⁹⁴(95-digit number)
25762706576108381250…53533970998552806920
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
2.576 Γ— 10⁹⁴(95-digit number)
25762706576108381250…53533970998552806919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.152 Γ— 10⁹⁴(95-digit number)
51525413152216762501…07067941997105613839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.030 Γ— 10⁹⁡(96-digit number)
10305082630443352500…14135883994211227679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.061 Γ— 10⁹⁡(96-digit number)
20610165260886705000…28271767988422455359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.122 Γ— 10⁹⁡(96-digit number)
41220330521773410000…56543535976844910719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.244 Γ— 10⁹⁡(96-digit number)
82440661043546820001…13087071953689821439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.648 Γ— 10⁹⁢(97-digit number)
16488132208709364000…26174143907379642879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.297 Γ— 10⁹⁢(97-digit number)
32976264417418728000…52348287814759285759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.595 Γ— 10⁹⁢(97-digit number)
65952528834837456001…04696575629518571519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.319 Γ— 10⁹⁷(98-digit number)
13190505766967491200…09393151259037143039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.638 Γ— 10⁹⁷(98-digit number)
26381011533934982400…18786302518074286079
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 2144271

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 4e84cac958c0b820573820c2abe5e638c64b94fe1c5a74ef6b84d71ddaf3cabb

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 #2,144,271 on Chainz β†—
Circulating Supply:57,987,393 XPMΒ·at block #6,842,880 Β· updates every 60s
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