Home/Chain Registry/Block #449,029

Block #449,029

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/18/2014, 8:25:41 AM · Difficulty 10.3578 · 6,357,054 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6502e94a4e6b4a83f7b78076cc4bdcc5c05ff3263e5c452dfb8be75fb642a3cb

Height

#449,029

Difficulty

10.357786

Transactions

12

Size

3.60 KB

Version

2

Bits

0a5b97da

Nonce

6,050

Timestamp

3/18/2014, 8:25:41 AM

Confirmations

6,357,054

Merkle Root

f02a2f7a157d2473ea52114064efa8b83eb9c20685574cd0c6dac90b305ac77c
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.066 × 10⁹³(94-digit number)
10662549044267877951…25216981569730954600
Discovered Prime Numbers
p_k = 2^k × 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
1.066 × 10⁹³(94-digit number)
10662549044267877951…25216981569730954601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.132 × 10⁹³(94-digit number)
21325098088535755903…50433963139461909201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.265 × 10⁹³(94-digit number)
42650196177071511806…00867926278923818401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.530 × 10⁹³(94-digit number)
85300392354143023613…01735852557847636801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.706 × 10⁹⁴(95-digit number)
17060078470828604722…03471705115695273601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.412 × 10⁹⁴(95-digit number)
34120156941657209445…06943410231390547201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.824 × 10⁹⁴(95-digit number)
68240313883314418891…13886820462781094401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.364 × 10⁹⁵(96-digit number)
13648062776662883778…27773640925562188801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.729 × 10⁹⁵(96-digit number)
27296125553325767556…55547281851124377601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.459 × 10⁹⁵(96-digit number)
54592251106651535112…11094563702248755201
Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — 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 →
★★☆☆☆
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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 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 449029

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 6502e94a4e6b4a83f7b78076cc4bdcc5c05ff3263e5c452dfb8be75fb642a3cb

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 → Debug Window → 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 #449,029 on Chainz ↗
Circulating Supply:57,692,736 XPM·at block #6,806,082 · updates every 60s
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