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Home/Chain Registry/Block #847,119

Block #847,119

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/10/2014, 3:11:02 AM Β· Difficulty 10.9719 Β· 5,993,961 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f0cff986244f76d824a3bf201f0821e5eeb1f4f3e2eeb54082059f14b2ca9618
View on Chainz β†—

Height

#847,119

Difficulty

10.971925

Transactions

1

Size

242 B

Version

2

Bits

0af8d016

Nonce

3,080,173,803

Timestamp

12/10/2014, 3:11:02 AM

Confirmations

5,993,961

Merkle Root

a3825125b349822dd593dd651b6f4d5838eb3cf3eb4c4fca91b44be200de0947
Transactions (1)
Coinbasea3825125b34982…b44be200de0947
1 in β†’ 2 out8.2900 XPM152 B
AUiL5uhi…95n9aZH6ALPu3s2c…EJXLjVFh
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.

2.605 Γ— 10⁹³(94-digit number)
26054477223941263740…93351897237432219580
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
2.605 Γ— 10⁹³(94-digit number)
26054477223941263740…93351897237432219581
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.210 Γ— 10⁹³(94-digit number)
52108954447882527480…86703794474864439161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.042 Γ— 10⁹⁴(95-digit number)
10421790889576505496…73407588949728878321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.084 Γ— 10⁹⁴(95-digit number)
20843581779153010992…46815177899457756641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.168 Γ— 10⁹⁴(95-digit number)
41687163558306021984…93630355798915513281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.337 Γ— 10⁹⁴(95-digit number)
83374327116612043969…87260711597831026561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.667 Γ— 10⁹⁡(96-digit number)
16674865423322408793…74521423195662053121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.334 Γ— 10⁹⁡(96-digit number)
33349730846644817587…49042846391324106241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.669 Γ— 10⁹⁡(96-digit number)
66699461693289635175…98085692782648212481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.333 Γ— 10⁹⁢(97-digit number)
13339892338657927035…96171385565296424961
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 847119

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 f0cff986244f76d824a3bf201f0821e5eeb1f4f3e2eeb54082059f14b2ca9618

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 #847,119 on Chainz β†—
Circulating Supply:57,973,002 XPMΒ·at block #6,841,079 Β· updates every 60s
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