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Block #840,756

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/5/2014, 9:23:59 AM Β· Difficulty 10.9742 Β· 6,004,503 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dcee93e77b6267819e9902fc82bcd1b95874e0e40d2401cc0bdced3a09e03d33
View on Chainz β†—

Height

#840,756

Difficulty

10.974212

Transactions

2

Size

398 B

Version

2

Bits

0af965f9

Nonce

117,421,030

Timestamp

12/5/2014, 9:23:59 AM

Confirmations

6,004,503

Merkle Root

34a9beb9095701ca057a35924d8dbddac5993bb63a2752fe5b4d007514a1cdd7
Transactions (2)
Coinbase72d57fb4281229…218e4efc97881b
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
7c575ce76d6203…05b8a2fbf8061a
1 in β†’ 2 out8.2800 XPM192 B
AUtVyZQv…vn1RwywSAMN6qDkt…VuvvTq6f
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.

2.374 Γ— 10⁹⁡(96-digit number)
23741069797950701810…09862242433270567060
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
2.374 Γ— 10⁹⁡(96-digit number)
23741069797950701810…09862242433270567061
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.748 Γ— 10⁹⁡(96-digit number)
47482139595901403620…19724484866541134121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.496 Γ— 10⁹⁡(96-digit number)
94964279191802807240…39448969733082268241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.899 Γ— 10⁹⁢(97-digit number)
18992855838360561448…78897939466164536481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.798 Γ— 10⁹⁢(97-digit number)
37985711676721122896…57795878932329072961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.597 Γ— 10⁹⁢(97-digit number)
75971423353442245792…15591757864658145921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.519 Γ— 10⁹⁷(98-digit number)
15194284670688449158…31183515729316291841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.038 Γ— 10⁹⁷(98-digit number)
30388569341376898317…62367031458632583681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.077 Γ— 10⁹⁷(98-digit number)
60777138682753796634…24734062917265167361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.215 Γ— 10⁹⁸(99-digit number)
12155427736550759326…49468125834530334721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.431 Γ— 10⁹⁸(99-digit number)
24310855473101518653…98936251669060669441
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 840756

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 dcee93e77b6267819e9902fc82bcd1b95874e0e40d2401cc0bdced3a09e03d33

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 #840,756 on Chainz β†—
Circulating Supply:58,006,505 XPMΒ·at block #6,845,258 Β· updates every 60s
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