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Home/Chain Registry/Block #394,582

Block #394,582

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/8/2014, 1:57:56 AM Β· Difficulty 10.4194 Β· 6,410,407 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
00a9f2f1627e38191dae82ba3e916a6fd4377d81008faaed40737fd09d3a9b66
View on Chainz β†—

Height

#394,582

Difficulty

10.419382

Transactions

2

Size

427 B

Version

2

Bits

0a6b5c9b

Nonce

51,354

Timestamp

2/8/2014, 1:57:56 AM

Confirmations

6,410,407

Merkle Root

d64aff0574f2cc4ecf59e7d08bca5e718d40329c39e47f7db2b68a68e0430184
Transactions (2)
Coinbase4d7bc4308dd766…3114ae19091df5
1 in β†’ 1 out9.2100 XPM109 B
ARZ8824u…4fgdP6we
7ec9d6bcfd3ec5…2eee312a018f19
1 in β†’ 2 out112.7021 XPM227 B
AGiK7Y5F…aPV8HpCtAJQVbzAJ…n6NHm8ig
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.

1.506 Γ— 10⁹⁸(99-digit number)
15063007955329717352…17941734858824682880
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
1.506 Γ— 10⁹⁸(99-digit number)
15063007955329717352…17941734858824682879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.012 Γ— 10⁹⁸(99-digit number)
30126015910659434705…35883469717649365759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.025 Γ— 10⁹⁸(99-digit number)
60252031821318869410…71766939435298731519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.205 Γ— 10⁹⁹(100-digit number)
12050406364263773882…43533878870597463039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.410 Γ— 10⁹⁹(100-digit number)
24100812728527547764…87067757741194926079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.820 Γ— 10⁹⁹(100-digit number)
48201625457055095528…74135515482389852159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.640 Γ— 10⁹⁹(100-digit number)
96403250914110191057…48271030964779704319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.928 Γ— 10¹⁰⁰(101-digit number)
19280650182822038211…96542061929559408639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.856 Γ— 10¹⁰⁰(101-digit number)
38561300365644076422…93084123859118817279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.712 Γ— 10¹⁰⁰(101-digit number)
77122600731288152845…86168247718237634559
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 394582

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 00a9f2f1627e38191dae82ba3e916a6fd4377d81008faaed40737fd09d3a9b66

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 #394,582 on Chainz β†—
Circulating Supply:57,683,981 XPMΒ·at block #6,804,988 Β· updates every 60s
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