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Block #449,832

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/18/2014, 9:03:55 PM Β· Difficulty 10.3721 Β· 6,392,137 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e39451814ddea90dd3bb4156530f6625fee2e7140b6a7ea140bf87a21c9bcd06
View on Chainz β†—

Height

#449,832

Difficulty

10.372053

Transactions

1

Size

200 B

Version

2

Bits

0a5f3ed9

Nonce

11,157,094

Timestamp

3/18/2014, 9:03:55 PM

Confirmations

6,392,137

Merkle Root

d849c233b5ab79da0f67594141d7d6023ca72cc98dba9f25f66f2fcca137ffe5
Transactions (1)
Coinbased849c233b5ab79…6f2fcca137ffe5
1 in β†’ 1 out9.2800 XPM110 B
APovXh4d…CNGGgZjQ
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.

3.316 Γ— 10⁹⁡(96-digit number)
33168741551220948417…50396002576367838560
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
3.316 Γ— 10⁹⁡(96-digit number)
33168741551220948417…50396002576367838561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.633 Γ— 10⁹⁡(96-digit number)
66337483102441896834…00792005152735677121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.326 Γ— 10⁹⁢(97-digit number)
13267496620488379366…01584010305471354241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.653 Γ— 10⁹⁢(97-digit number)
26534993240976758733…03168020610942708481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.306 Γ— 10⁹⁢(97-digit number)
53069986481953517467…06336041221885416961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.061 Γ— 10⁹⁷(98-digit number)
10613997296390703493…12672082443770833921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.122 Γ— 10⁹⁷(98-digit number)
21227994592781406987…25344164887541667841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.245 Γ— 10⁹⁷(98-digit number)
42455989185562813974…50688329775083335681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.491 Γ— 10⁹⁷(98-digit number)
84911978371125627948…01376659550166671361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.698 Γ— 10⁹⁸(99-digit number)
16982395674225125589…02753319100333342721
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 449832

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 e39451814ddea90dd3bb4156530f6625fee2e7140b6a7ea140bf87a21c9bcd06

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 #449,832 on Chainz β†—
Circulating Supply:57,980,135 XPMΒ·at block #6,841,968 Β· updates every 60s
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