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Block #401,458

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/12/2014, 6:42:48 PM Β· Difficulty 10.4348 Β· 6,425,224 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bb8839a87e6f47cfc8ce25b1706f8c88ffde2382ffac6683772d5bbacc078774
View on Chainz β†—

Height

#401,458

Difficulty

10.434757

Transactions

1

Size

207 B

Version

2

Bits

0a6f4c3c

Nonce

80,259

Timestamp

2/12/2014, 6:42:48 PM

Confirmations

6,425,224

Merkle Root

8dec7b345234997b9234ad67977a050dbff79ddca09e22b6aad93ee71d2bedda
Transactions (1)
Coinbase8dec7b34523499…d93ee71d2bedda
1 in β†’ 1 out9.1700 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.

2.955 Γ— 10⁹⁷(98-digit number)
29554297102561311287…07289402021321856000
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
2.955 Γ— 10⁹⁷(98-digit number)
29554297102561311287…07289402021321856001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.910 Γ— 10⁹⁷(98-digit number)
59108594205122622574…14578804042643712001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.182 Γ— 10⁹⁸(99-digit number)
11821718841024524514…29157608085287424001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.364 Γ— 10⁹⁸(99-digit number)
23643437682049049029…58315216170574848001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.728 Γ— 10⁹⁸(99-digit number)
47286875364098098059…16630432341149696001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.457 Γ— 10⁹⁸(99-digit number)
94573750728196196118…33260864682299392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.891 Γ— 10⁹⁹(100-digit number)
18914750145639239223…66521729364598784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.782 Γ— 10⁹⁹(100-digit number)
37829500291278478447…33043458729197568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.565 Γ— 10⁹⁹(100-digit number)
75659000582556956895…66086917458395136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.513 Γ— 10¹⁰⁰(101-digit number)
15131800116511391379…32173834916790272001
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 401458

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 bb8839a87e6f47cfc8ce25b1706f8c88ffde2382ffac6683772d5bbacc078774

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 #401,458 on Chainz β†—
Circulating Supply:57,857,605 XPMΒ·at block #6,826,681 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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