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Block #2,280,291

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/3/2017, 5:40:47 AM Β· Difficulty 10.9561 Β· 4,561,942 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d8906e80e57e4a00ba5f8459d845676637cb4564d2dea614863e72fa5ab1142f
View on Chainz β†—

Difficulty

10.956112

Transactions

1

Size

199 B

Version

2

Bits

0af4c3c8

Nonce

1,551,780,988

Timestamp

9/3/2017, 5:40:47 AM

Confirmations

4,561,942

Merkle Root

af0998b4a1dba5e79f022f1347c9b98648dbbfab720c925ae42f84feac871471
Transactions (1)
Coinbaseaf0998b4a1dba5…2f84feac871471
1 in β†’ 1 out8.3200 XPM109 B
AQgcUg2K…graUZdXG
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.

1.602 Γ— 10⁹⁴(95-digit number)
16024422339592453960…21070400923024931840
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.602 Γ— 10⁹⁴(95-digit number)
16024422339592453960…21070400923024931841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.204 Γ— 10⁹⁴(95-digit number)
32048844679184907920…42140801846049863681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.409 Γ— 10⁹⁴(95-digit number)
64097689358369815840…84281603692099727361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.281 Γ— 10⁹⁡(96-digit number)
12819537871673963168…68563207384199454721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.563 Γ— 10⁹⁡(96-digit number)
25639075743347926336…37126414768398909441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.127 Γ— 10⁹⁡(96-digit number)
51278151486695852672…74252829536797818881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.025 Γ— 10⁹⁢(97-digit number)
10255630297339170534…48505659073595637761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.051 Γ— 10⁹⁢(97-digit number)
20511260594678341068…97011318147191275521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.102 Γ— 10⁹⁢(97-digit number)
41022521189356682137…94022636294382551041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.204 Γ— 10⁹⁢(97-digit number)
82045042378713364275…88045272588765102081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.640 Γ— 10⁹⁷(98-digit number)
16409008475742672855…76090545177530204161
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2280291

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 d8906e80e57e4a00ba5f8459d845676637cb4564d2dea614863e72fa5ab1142f

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 #2,280,291 on Chainz β†—
Circulating Supply:57,982,264 XPMΒ·at block #6,842,232 Β· updates every 60s
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