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Block #449,088

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/18/2014, 9:17:00 AM Β· Difficulty 10.3672 Β· 6,363,391 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
936ddb9f3c55f62065c767edf2ba608e477f2532bf3e456a834838c2c8277ada
View on Chainz β†—

Height

#449,088

Difficulty

10.367235

Transactions

1

Size

187 B

Version

2

Bits

0a5e0315

Nonce

259,743

Timestamp

3/18/2014, 9:17:00 AM

Confirmations

6,363,391

Merkle Root

4ca342c013253d2285644d9fe10d30756e0c02edc7182b3d2c31001449ed61d6
Transactions (1)
Coinbase4ca342c013253d…31001449ed61d6
1 in β†’ 1 out9.2900 XPM97 B
AbMAHMS8…MwEzMSoj
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.

2.726 Γ— 10⁹³(94-digit number)
27269299550529835410…34949075604627190280
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
2.726 Γ— 10⁹³(94-digit number)
27269299550529835410…34949075604627190281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.453 Γ— 10⁹³(94-digit number)
54538599101059670820…69898151209254380561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.090 Γ— 10⁹⁴(95-digit number)
10907719820211934164…39796302418508761121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.181 Γ— 10⁹⁴(95-digit number)
21815439640423868328…79592604837017522241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.363 Γ— 10⁹⁴(95-digit number)
43630879280847736656…59185209674035044481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.726 Γ— 10⁹⁴(95-digit number)
87261758561695473313…18370419348070088961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.745 Γ— 10⁹⁡(96-digit number)
17452351712339094662…36740838696140177921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.490 Γ— 10⁹⁡(96-digit number)
34904703424678189325…73481677392280355841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.980 Γ— 10⁹⁡(96-digit number)
69809406849356378650…46963354784560711681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.396 Γ— 10⁹⁢(97-digit number)
13961881369871275730…93926709569121423361
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 449088

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 936ddb9f3c55f62065c767edf2ba608e477f2532bf3e456a834838c2c8277ada

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 #449,088 on Chainz β†—
Circulating Supply:57,743,860 XPMΒ·at block #6,812,478 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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