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Home/Chain Registry/Block #2,114,108

Block #2,114,108

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/13/2017, 10:34:04 AM Β· Difficulty 10.8997 Β· 4,710,880 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4b78883e636cf9a8e7613be2e6a849fb2dbf39839251d39a70a2acacb0a04f9c
View on Chainz β†—

Difficulty

10.899710

Transactions

1

Size

201 B

Version

2

Bits

0ae65360

Nonce

1,025,470,651

Timestamp

5/13/2017, 10:34:04 AM

Confirmations

4,710,880

Merkle Root

17d4d606bf7baa6e0d51eb6688a8da9458a3887f671cec493f877d9dd9a1b771
Transactions (1)
Coinbase17d4d606bf7baa…877d9dd9a1b771
1 in β†’ 1 out8.4000 XPM110 B
AXM7cFP8…yqB6oAGG
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.

2.305 Γ— 10⁹⁢(97-digit number)
23055895340200630285…38974228474892815360
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
2.305 Γ— 10⁹⁢(97-digit number)
23055895340200630285…38974228474892815359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.611 Γ— 10⁹⁢(97-digit number)
46111790680401260571…77948456949785630719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.222 Γ— 10⁹⁢(97-digit number)
92223581360802521143…55896913899571261439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.844 Γ— 10⁹⁷(98-digit number)
18444716272160504228…11793827799142522879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.688 Γ— 10⁹⁷(98-digit number)
36889432544321008457…23587655598285045759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.377 Γ— 10⁹⁷(98-digit number)
73778865088642016914…47175311196570091519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.475 Γ— 10⁹⁸(99-digit number)
14755773017728403382…94350622393140183039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.951 Γ— 10⁹⁸(99-digit number)
29511546035456806765…88701244786280366079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.902 Γ— 10⁹⁸(99-digit number)
59023092070913613531…77402489572560732159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.180 Γ— 10⁹⁹(100-digit number)
11804618414182722706…54804979145121464319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2114108

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 4b78883e636cf9a8e7613be2e6a849fb2dbf39839251d39a70a2acacb0a04f9c

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 #2,114,108 on Chainz β†—
Circulating Supply:57,843,987 XPMΒ·at block #6,824,987 Β· updates every 60s
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