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Block #359,545

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/14/2014, 8:47:27 PM Β· Difficulty 10.3884 Β· 6,441,507 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5a67fa2fef7026098679e3c4208199cfe2f1c6bc8005857e54873e221aa0d606
View on Chainz β†—

Height

#359,545

Difficulty

10.388421

Transactions

1

Size

207 B

Version

2

Bits

0a636f90

Nonce

4,443

Timestamp

1/14/2014, 8:47:27 PM

Confirmations

6,441,507

Merkle Root

424f0a5e42120072b125a61f2dedc0194e41e12384a3ff665fbce77d7142fffa
Transactions (1)
Coinbase424f0a5e421200…bce77d7142fffa
1 in β†’ 1 out9.2500 XPM116 B
AbwWkWZt…kawDhufa
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.

8.334 Γ— 10⁹⁢(97-digit number)
83348709455610196909…36669152506616189520
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
8.334 Γ— 10⁹⁢(97-digit number)
83348709455610196909…36669152506616189521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.666 Γ— 10⁹⁷(98-digit number)
16669741891122039381…73338305013232379041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.333 Γ— 10⁹⁷(98-digit number)
33339483782244078763…46676610026464758081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.667 Γ— 10⁹⁷(98-digit number)
66678967564488157527…93353220052929516161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.333 Γ— 10⁹⁸(99-digit number)
13335793512897631505…86706440105859032321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.667 Γ— 10⁹⁸(99-digit number)
26671587025795263010…73412880211718064641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.334 Γ— 10⁹⁸(99-digit number)
53343174051590526021…46825760423436129281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.066 Γ— 10⁹⁹(100-digit number)
10668634810318105204…93651520846872258561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.133 Γ— 10⁹⁹(100-digit number)
21337269620636210408…87303041693744517121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.267 Γ— 10⁹⁹(100-digit number)
42674539241272420817…74606083387489034241
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 359545

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 5a67fa2fef7026098679e3c4208199cfe2f1c6bc8005857e54873e221aa0d606

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 #359,545 on Chainz β†—
Circulating Supply:57,652,482 XPMΒ·at block #6,801,051 Β· updates every 60s
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