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Block #457,376

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/23/2014, 8:48:57 PM Β· Difficulty 10.4201 Β· 6,369,557 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0e677acb97b4e5f2024b38e0fb9b492364c5c3627b5948dc66dc69ffe377e1b0
View on Chainz β†—

Height

#457,376

Difficulty

10.420114

Transactions

1

Size

206 B

Version

2

Bits

0a6b8c9f

Nonce

1,668

Timestamp

3/23/2014, 8:48:57 PM

Confirmations

6,369,557

Merkle Root

ecf0fa0d8bd7ba35652bcd8f9d15fa1c0784aea22f3413fb4c7daab1099b2190
Transactions (1)
Coinbaseecf0fa0d8bd7ba…7daab1099b2190
1 in β†’ 1 out9.2000 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.

4.942 Γ— 10⁹⁴(95-digit number)
49422722152354098120…34549950668209586560
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.942 Γ— 10⁹⁴(95-digit number)
49422722152354098120…34549950668209586559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.884 Γ— 10⁹⁴(95-digit number)
98845444304708196241…69099901336419173119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.976 Γ— 10⁹⁡(96-digit number)
19769088860941639248…38199802672838346239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.953 Γ— 10⁹⁡(96-digit number)
39538177721883278496…76399605345676692479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.907 Γ— 10⁹⁡(96-digit number)
79076355443766556992…52799210691353384959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.581 Γ— 10⁹⁢(97-digit number)
15815271088753311398…05598421382706769919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.163 Γ— 10⁹⁢(97-digit number)
31630542177506622797…11196842765413539839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.326 Γ— 10⁹⁢(97-digit number)
63261084355013245594…22393685530827079679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.265 Γ— 10⁹⁷(98-digit number)
12652216871002649118…44787371061654159359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.530 Γ— 10⁹⁷(98-digit number)
25304433742005298237…89574742123308318719
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 457376

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 0e677acb97b4e5f2024b38e0fb9b492364c5c3627b5948dc66dc69ffe377e1b0

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 #457,376 on Chainz β†—
Circulating Supply:57,859,636 XPMΒ·at block #6,826,932 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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