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Home/Chain Registry/Block #2,190,365

Block #2,190,365

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/3/2017, 2:06:17 AM Β· Difficulty 10.9495 Β· 4,636,525 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
eab2df54ae7f20a75e1eca5f0919465bb96ba395d9edf263741d72451a647d8d
View on Chainz β†—

Difficulty

10.949529

Transactions

1

Size

200 B

Version

2

Bits

0af3145a

Nonce

1,811,882,704

Timestamp

7/3/2017, 2:06:17 AM

Confirmations

4,636,525

Merkle Root

c3d91c400085289118cb44b99d6ded00389371601c4bbe6cefa75fd42190d3f0
Transactions (1)
Coinbasec3d91c40008528…a75fd42190d3f0
1 in β†’ 1 out8.3300 XPM110 B
AR7c1Y1G…76e1Qap3
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.

3.008 Γ— 10⁹⁴(95-digit number)
30084637158142825026…84371944013879855360
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
3.008 Γ— 10⁹⁴(95-digit number)
30084637158142825026…84371944013879855359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.016 Γ— 10⁹⁴(95-digit number)
60169274316285650052…68743888027759710719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.203 Γ— 10⁹⁡(96-digit number)
12033854863257130010…37487776055519421439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.406 Γ— 10⁹⁡(96-digit number)
24067709726514260021…74975552111038842879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.813 Γ— 10⁹⁡(96-digit number)
48135419453028520042…49951104222077685759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.627 Γ— 10⁹⁡(96-digit number)
96270838906057040084…99902208444155371519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.925 Γ— 10⁹⁢(97-digit number)
19254167781211408016…99804416888310743039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.850 Γ— 10⁹⁢(97-digit number)
38508335562422816033…99608833776621486079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.701 Γ— 10⁹⁢(97-digit number)
77016671124845632067…99217667553242972159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.540 Γ— 10⁹⁷(98-digit number)
15403334224969126413…98435335106485944319
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 2190365

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 eab2df54ae7f20a75e1eca5f0919465bb96ba395d9edf263741d72451a647d8d

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 #2,190,365 on Chainz β†—
Circulating Supply:57,859,285 XPMΒ·at block #6,826,889 Β· updates every 60s
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