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Block #358,815

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/14/2014, 9:10:32 AM Β· Difficulty 10.3840 Β· 6,455,535 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d355ccc5507066a76b2c29753cd5142191505ccffd0e69dea238e05c278dc629
View on Chainz β†—

Height

#358,815

Difficulty

10.383992

Transactions

2

Size

542 B

Version

2

Bits

0a624d48

Nonce

764,617

Timestamp

1/14/2014, 9:10:32 AM

Confirmations

6,455,535

Merkle Root

94da1ee097dbf6241d8202f3cb3183c6132daf283bc636dbc54c443906c04f95
Transactions (2)
Coinbased2e224901db172…eedbbdf26585d2
1 in β†’ 1 out9.2700 XPM110 B
AeKNrjNj…1NEq95Ta
b668c9325335bf…802945e669df96
2 in β†’ 1 out5.9800 XPM341 B
ALd1X1C1…4FNBqzHN
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.

2.566 Γ— 10⁹⁷(98-digit number)
25664922804996450019…29940483613312211200
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
2.566 Γ— 10⁹⁷(98-digit number)
25664922804996450019…29940483613312211201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.132 Γ— 10⁹⁷(98-digit number)
51329845609992900038…59880967226624422401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.026 Γ— 10⁹⁸(99-digit number)
10265969121998580007…19761934453248844801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.053 Γ— 10⁹⁸(99-digit number)
20531938243997160015…39523868906497689601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.106 Γ— 10⁹⁸(99-digit number)
41063876487994320031…79047737812995379201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.212 Γ— 10⁹⁸(99-digit number)
82127752975988640062…58095475625990758401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.642 Γ— 10⁹⁹(100-digit number)
16425550595197728012…16190951251981516801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.285 Γ— 10⁹⁹(100-digit number)
32851101190395456024…32381902503963033601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.570 Γ— 10⁹⁹(100-digit number)
65702202380790912049…64763805007926067201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.314 Γ— 10¹⁰⁰(101-digit number)
13140440476158182409…29527610015852134401
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 358815

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 d355ccc5507066a76b2c29753cd5142191505ccffd0e69dea238e05c278dc629

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 #358,815 on Chainz β†—
Circulating Supply:57,758,864 XPMΒ·at block #6,814,349 Β· updates every 60s
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