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Home/Chain Registry/Block #2,286,589

Block #2,286,589

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/7/2017, 4:21:05 PM Β· Difficulty 10.9554 Β· 4,552,586 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
942ed6efadeb92b34da333ec0676fd3c0ce81444c08487b20f825cb2125466b6
View on Chainz β†—

Difficulty

10.955399

Transactions

2

Size

872 B

Version

2

Bits

0af49506

Nonce

287,433,762

Timestamp

9/7/2017, 4:21:05 PM

Confirmations

4,552,586

Merkle Root

1c511d8f00af489a6543014e96bda012055d500990ba44bbd977c1611de9ad21
Transactions (2)
Coinbase859d6d4fe8768b…81d8abde46c650
1 in β†’ 1 out8.3300 XPM110 B
AYMogixN…89zi42rj
fb35411419faf6…eaec2dbac9cb4c
4 in β†’ 2 out23.3735 XPM672 B
AdBcgmf2…WkkJwZP2ASw6rAQU…eiz69c1J
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.

1.076 Γ— 10⁹⁡(96-digit number)
10767112597532595076…47486434803690133600
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
1.076 Γ— 10⁹⁡(96-digit number)
10767112597532595076…47486434803690133601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.153 Γ— 10⁹⁡(96-digit number)
21534225195065190152…94972869607380267201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.306 Γ— 10⁹⁡(96-digit number)
43068450390130380304…89945739214760534401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.613 Γ— 10⁹⁡(96-digit number)
86136900780260760608…79891478429521068801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.722 Γ— 10⁹⁢(97-digit number)
17227380156052152121…59782956859042137601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.445 Γ— 10⁹⁢(97-digit number)
34454760312104304243…19565913718084275201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.890 Γ— 10⁹⁢(97-digit number)
68909520624208608486…39131827436168550401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.378 Γ— 10⁹⁷(98-digit number)
13781904124841721697…78263654872337100801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.756 Γ— 10⁹⁷(98-digit number)
27563808249683443394…56527309744674201601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.512 Γ— 10⁹⁷(98-digit number)
55127616499366886789…13054619489348403201
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 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
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 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 2286589

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 942ed6efadeb92b34da333ec0676fd3c0ce81444c08487b20f825cb2125466b6

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 #2,286,589 on Chainz β†—
Circulating Supply:57,957,682 XPMΒ·at block #6,839,174 Β· updates every 60s
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