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Home/Chain Registry/Block #357,831

Block #357,831

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/13/2014, 4:08:23 PM Β· Difficulty 10.3882 Β· 6,454,626 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eb18ec4e1cea8a9b94df61f4f45fe8478ce49ff562cb4e6e7ff8114aa111184a
View on Chainz β†—

Height

#357,831

Difficulty

10.388171

Transactions

1

Size

201 B

Version

2

Bits

0a635f2a

Nonce

16,900

Timestamp

1/13/2014, 4:08:23 PM

Confirmations

6,454,626

Merkle Root

47455e045aee46b8618147fbf4377b91d5407fd61888c08b8fc7d2da7e8da2c3
Transactions (1)
Coinbase47455e045aee46…c7d2da7e8da2c3
1 in β†’ 1 out9.2500 XPM109 B
AUqLo922…kfXxP716
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.

5.227 Γ— 10¹⁰⁰(101-digit number)
52270460838337266682…03423016526968422400
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
5.227 Γ— 10¹⁰⁰(101-digit number)
52270460838337266682…03423016526968422401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.045 Γ— 10¹⁰¹(102-digit number)
10454092167667453336…06846033053936844801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.090 Γ— 10¹⁰¹(102-digit number)
20908184335334906672…13692066107873689601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.181 Γ— 10¹⁰¹(102-digit number)
41816368670669813345…27384132215747379201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.363 Γ— 10¹⁰¹(102-digit number)
83632737341339626691…54768264431494758401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.672 Γ— 10¹⁰²(103-digit number)
16726547468267925338…09536528862989516801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.345 Γ— 10¹⁰²(103-digit number)
33453094936535850676…19073057725979033601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.690 Γ— 10¹⁰²(103-digit number)
66906189873071701353…38146115451958067201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.338 Γ— 10¹⁰³(104-digit number)
13381237974614340270…76292230903916134401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.676 Γ— 10¹⁰³(104-digit number)
26762475949228680541…52584461807832268801
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 357831

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 eb18ec4e1cea8a9b94df61f4f45fe8478ce49ff562cb4e6e7ff8114aa111184a

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 #357,831 on Chainz β†—
Circulating Supply:57,743,681 XPMΒ·at block #6,812,456 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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