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Home/Chain Registry/Block #2,290,649

Block #2,290,649

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2017, 12:29:48 PM Β· Difficulty 10.9553 Β· 4,546,478 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1a1903366ab777774bcf1118aeda344adb6ba80b0fdae0057cf0e43a04df41c0
View on Chainz β†—

Difficulty

10.955272

Transactions

1

Size

200 B

Version

2

Bits

0af48cbc

Nonce

752,004,535

Timestamp

9/10/2017, 12:29:48 PM

Confirmations

4,546,478

Merkle Root

d6924d98b20d5f96decee99fdf246a495487343c26d4f3e9e21bb0eac1550662
Transactions (1)
Coinbased6924d98b20d5f…1bb0eac1550662
1 in β†’ 1 out8.3200 XPM110 B
AQDRgKwy…fwdLQirb
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.

1.003 Γ— 10⁹⁴(95-digit number)
10030200027747838563…85485914066527906480
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
1.003 Γ— 10⁹⁴(95-digit number)
10030200027747838563…85485914066527906479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.006 Γ— 10⁹⁴(95-digit number)
20060400055495677127…70971828133055812959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.012 Γ— 10⁹⁴(95-digit number)
40120800110991354254…41943656266111625919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.024 Γ— 10⁹⁴(95-digit number)
80241600221982708509…83887312532223251839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.604 Γ— 10⁹⁡(96-digit number)
16048320044396541701…67774625064446503679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.209 Γ— 10⁹⁡(96-digit number)
32096640088793083403…35549250128893007359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.419 Γ— 10⁹⁡(96-digit number)
64193280177586166807…71098500257786014719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.283 Γ— 10⁹⁢(97-digit number)
12838656035517233361…42197000515572029439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.567 Γ— 10⁹⁢(97-digit number)
25677312071034466723…84394001031144058879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.135 Γ— 10⁹⁢(97-digit number)
51354624142068933446…68788002062288117759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.027 Γ— 10⁹⁷(98-digit number)
10270924828413786689…37576004124576235519
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 2290649

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 1a1903366ab777774bcf1118aeda344adb6ba80b0fdae0057cf0e43a04df41c0

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 #2,290,649 on Chainz β†—
Circulating Supply:57,941,325 XPMΒ·at block #6,837,126 Β· updates every 60s
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