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Home/Chain Registry/Block #2,880,209

Block #2,880,209

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/14/2018, 3:18:41 AM Β· Difficulty 11.6336 Β· 3,957,078 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
37ccdac845214805112fd719898b0eb28a53bec8737c82e7cc6c1a1c5040973a
View on Chainz β†—

Difficulty

11.633570

Transactions

2

Size

575 B

Version

2

Bits

0ba231a7

Nonce

175,688,788

Timestamp

10/14/2018, 3:18:41 AM

Confirmations

3,957,078

Merkle Root

eea5ff8554c464e0f45412781c4782c8bed779891310092211a107cc8a72d3e2
Transactions (2)
Coinbase1eab2259f4d0e2…2acdcdafd6bb8f
1 in β†’ 1 out7.3900 XPM110 B
AaYE7Psb…doS6TEGu
8eeac4fd464567…71885e72fc860a
2 in β†’ 2 out4.1082 XPM374 B
AbedDeps…sRvZfRkkAH2V7fKW…AL3qjzq1
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.

7.922 Γ— 10⁹⁡(96-digit number)
79227759144768732906…60632417497191267840
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
7.922 Γ— 10⁹⁡(96-digit number)
79227759144768732906…60632417497191267841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.584 Γ— 10⁹⁢(97-digit number)
15845551828953746581…21264834994382535681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.169 Γ— 10⁹⁢(97-digit number)
31691103657907493162…42529669988765071361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.338 Γ— 10⁹⁢(97-digit number)
63382207315814986325…85059339977530142721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.267 Γ— 10⁹⁷(98-digit number)
12676441463162997265…70118679955060285441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.535 Γ— 10⁹⁷(98-digit number)
25352882926325994530…40237359910120570881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.070 Γ— 10⁹⁷(98-digit number)
50705765852651989060…80474719820241141761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.014 Γ— 10⁹⁸(99-digit number)
10141153170530397812…60949439640482283521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.028 Γ— 10⁹⁸(99-digit number)
20282306341060795624…21898879280964567041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.056 Γ— 10⁹⁸(99-digit number)
40564612682121591248…43797758561929134081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.112 Γ— 10⁹⁸(99-digit number)
81129225364243182496…87595517123858268161
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 2880209

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 37ccdac845214805112fd719898b0eb28a53bec8737c82e7cc6c1a1c5040973a

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 #2,880,209 on Chainz β†—
Circulating Supply:57,942,610 XPMΒ·at block #6,837,286 Β· updates every 60s
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