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Block #840,581

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/5/2014, 6:26:44 AM Β· Difficulty 10.9742 Β· 5,986,346 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
073d10f42480021572de9a9c7bb01ff8a716efa77dc0aa36fb6534d1672863ba
View on Chainz β†—

Height

#840,581

Difficulty

10.974217

Transactions

2

Size

431 B

Version

2

Bits

0af96643

Nonce

3,833,630,741

Timestamp

12/5/2014, 6:26:44 AM

Confirmations

5,986,346

Merkle Root

1499532be5d2501d4b11a72a762584f243199090d49a500a6d9c0162977391f2
Transactions (2)
Coinbase54d4c49630ab8f…9c54e13e109351
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
cf1e972e5d8566…cdab2a9bd0f3a0
1 in β†’ 2 out0.4828 XPM225 B
AKKr15k2…ptf7tYtSAMdg13ei…EVhNiPmU
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.

6.497 Γ— 10⁹⁴(95-digit number)
64978361400812605787…36194023648584308800
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
6.497 Γ— 10⁹⁴(95-digit number)
64978361400812605787…36194023648584308801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.299 Γ— 10⁹⁡(96-digit number)
12995672280162521157…72388047297168617601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.599 Γ— 10⁹⁡(96-digit number)
25991344560325042315…44776094594337235201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.198 Γ— 10⁹⁡(96-digit number)
51982689120650084630…89552189188674470401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.039 Γ— 10⁹⁢(97-digit number)
10396537824130016926…79104378377348940801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.079 Γ— 10⁹⁢(97-digit number)
20793075648260033852…58208756754697881601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.158 Γ— 10⁹⁢(97-digit number)
41586151296520067704…16417513509395763201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.317 Γ— 10⁹⁢(97-digit number)
83172302593040135408…32835027018791526401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.663 Γ— 10⁹⁷(98-digit number)
16634460518608027081…65670054037583052801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.326 Γ— 10⁹⁷(98-digit number)
33268921037216054163…31340108075166105601
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 840581

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 073d10f42480021572de9a9c7bb01ff8a716efa77dc0aa36fb6534d1672863ba

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 #840,581 on Chainz β†—
Circulating Supply:57,859,587 XPMΒ·at block #6,826,926 Β· updates every 60s
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