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Home/Chain Registry/Block #492,916

Block #492,916

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/15/2014, 10:31:56 AM Β· Difficulty 10.6916 Β· 6,333,410 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
06b56aa641b5489a35e8acdf133e6d40bfbfb0bb7b3b92558cdfddf007ad788b
View on Chainz β†—

Height

#492,916

Difficulty

10.691624

Transactions

1

Size

201 B

Version

2

Bits

0ab10e3d

Nonce

27,641

Timestamp

4/15/2014, 10:31:56 AM

Confirmations

6,333,410

Merkle Root

17658f06577f89a472dd971d15e6a1f5e6c7b1effad844b3dba7fdddaf69aa03
Transactions (1)
Coinbase17658f06577f89…a7fdddaf69aa03
1 in β†’ 1 out8.7300 XPM110 B
AKkc4exB…CKTSepvK
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.

3.148 Γ— 10⁹⁷(98-digit number)
31489721972487978966…79032668510519961600
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
3.148 Γ— 10⁹⁷(98-digit number)
31489721972487978966…79032668510519961601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.297 Γ— 10⁹⁷(98-digit number)
62979443944975957933…58065337021039923201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.259 Γ— 10⁹⁸(99-digit number)
12595888788995191586…16130674042079846401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.519 Γ— 10⁹⁸(99-digit number)
25191777577990383173…32261348084159692801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.038 Γ— 10⁹⁸(99-digit number)
50383555155980766346…64522696168319385601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.007 Γ— 10⁹⁹(100-digit number)
10076711031196153269…29045392336638771201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.015 Γ— 10⁹⁹(100-digit number)
20153422062392306538…58090784673277542401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.030 Γ— 10⁹⁹(100-digit number)
40306844124784613077…16181569346555084801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.061 Γ— 10⁹⁹(100-digit number)
80613688249569226154…32363138693110169601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.612 Γ— 10¹⁰⁰(101-digit number)
16122737649913845230…64726277386220339201
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 492916

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 06b56aa641b5489a35e8acdf133e6d40bfbfb0bb7b3b92558cdfddf007ad788b

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 #492,916 on Chainz β†—
Circulating Supply:57,854,748 XPMΒ·at block #6,826,325 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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