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Home/Chain Registry/Block #2,669,569

Block #2,669,569

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/20/2018, 7:37:09 AM Β· Difficulty 11.6791 Β· 4,163,091 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b2f61e3c43c2378fe0e67ec974a1456dd39799535b60c2d9c44f2e4b66733c2d
View on Chainz β†—

Difficulty

11.679128

Transactions

1

Size

199 B

Version

2

Bits

0baddb51

Nonce

413,710,841

Timestamp

5/20/2018, 7:37:09 AM

Confirmations

4,163,091

Merkle Root

74b55f303930a1f48b9b168b3bb79004df25fe465a2caa5b5c71e642a131319c
Transactions (1)
Coinbase74b55f303930a1…71e642a131319c
1 in β†’ 1 out7.3200 XPM109 B
Aeup7KZg…qu4ABYtd
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.

3.651 Γ— 10⁹³(94-digit number)
36512562121601367030…23156475853192152630
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
3.651 Γ— 10⁹³(94-digit number)
36512562121601367030…23156475853192152631
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.302 Γ— 10⁹³(94-digit number)
73025124243202734060…46312951706384305261
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.460 Γ— 10⁹⁴(95-digit number)
14605024848640546812…92625903412768610521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.921 Γ— 10⁹⁴(95-digit number)
29210049697281093624…85251806825537221041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.842 Γ— 10⁹⁴(95-digit number)
58420099394562187248…70503613651074442081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.168 Γ— 10⁹⁡(96-digit number)
11684019878912437449…41007227302148884161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.336 Γ— 10⁹⁡(96-digit number)
23368039757824874899…82014454604297768321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.673 Γ— 10⁹⁡(96-digit number)
46736079515649749798…64028909208595536641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.347 Γ— 10⁹⁡(96-digit number)
93472159031299499597…28057818417191073281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.869 Γ— 10⁹⁢(97-digit number)
18694431806259899919…56115636834382146561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.738 Γ— 10⁹⁢(97-digit number)
37388863612519799838…12231273668764293121
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 2669569

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 b2f61e3c43c2378fe0e67ec974a1456dd39799535b60c2d9c44f2e4b66733c2d

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 #2,669,569 on Chainz β†—
Circulating Supply:57,905,432 XPMΒ·at block #6,832,659 Β· updates every 60s
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