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Block #856,019

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/16/2014, 6:55:39 PM Β· Difficulty 10.9681 Β· 5,974,845 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
38985c896f7af2187a4563677231341ee6c6435bffb370bcc34905104ddfae63
View on Chainz β†—

Height

#856,019

Difficulty

10.968140

Transactions

1

Size

200 B

Version

2

Bits

0af7d805

Nonce

192,356,258

Timestamp

12/16/2014, 6:55:39 PM

Confirmations

5,974,845

Merkle Root

10760c40be856d9012cef02f6334f9f749dcce4295dbdb6e707dfa336c95b0ea
Transactions (1)
Coinbase10760c40be856d…7dfa336c95b0ea
1 in β†’ 1 out8.3000 XPM110 B
AKM6b4ti…oG8JQHWM
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.

6.564 Γ— 10⁹⁴(95-digit number)
65646965144142725378…29099557812509275520
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
6.564 Γ— 10⁹⁴(95-digit number)
65646965144142725378…29099557812509275521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.312 Γ— 10⁹⁡(96-digit number)
13129393028828545075…58199115625018551041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.625 Γ— 10⁹⁡(96-digit number)
26258786057657090151…16398231250037102081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.251 Γ— 10⁹⁡(96-digit number)
52517572115314180302…32796462500074204161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.050 Γ— 10⁹⁢(97-digit number)
10503514423062836060…65592925000148408321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.100 Γ— 10⁹⁢(97-digit number)
21007028846125672120…31185850000296816641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.201 Γ— 10⁹⁢(97-digit number)
42014057692251344241…62371700000593633281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.402 Γ— 10⁹⁢(97-digit number)
84028115384502688483…24743400001187266561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.680 Γ— 10⁹⁷(98-digit number)
16805623076900537696…49486800002374533121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.361 Γ— 10⁹⁷(98-digit number)
33611246153801075393…98973600004749066241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.722 Γ— 10⁹⁷(98-digit number)
67222492307602150787…97947200009498132481
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 856019

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 38985c896f7af2187a4563677231341ee6c6435bffb370bcc34905104ddfae63

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 #856,019 on Chainz β†—
Circulating Supply:57,891,050 XPMΒ·at block #6,830,863 Β· updates every 60s
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