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Home/Chain Registry/Block #404,984

Block #404,984

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/15/2014, 6:42:55 AM Β· Difficulty 10.4273 Β· 6,394,241 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
06f10c7db4673986e2752c281dc207e21b6d22a26e3a2f0371fa4cec4ff16562
View on Chainz β†—

Height

#404,984

Difficulty

10.427287

Transactions

1

Size

222 B

Version

2

Bits

0a6d62ae

Nonce

154,054

Timestamp

2/15/2014, 6:42:55 AM

Confirmations

6,394,241

Merkle Root

0ebbcfa9e699d92cda44adff738327ad7b6480f822cb702f508467907fd9cef2
Transactions (1)
Coinbase0ebbcfa9e699d9…8467907fd9cef2
1 in β†’ 2 out9.1800 XPM131 B
Ac2JYASP…tcBL5PEWAJno7LX2…vo4wdWtY
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.

2.720 Γ— 10⁹⁢(97-digit number)
27207957345509369212…54838594049462080140
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
2.720 Γ— 10⁹⁢(97-digit number)
27207957345509369212…54838594049462080139
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.441 Γ— 10⁹⁢(97-digit number)
54415914691018738425…09677188098924160279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.088 Γ— 10⁹⁷(98-digit number)
10883182938203747685…19354376197848320559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.176 Γ— 10⁹⁷(98-digit number)
21766365876407495370…38708752395696641119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.353 Γ— 10⁹⁷(98-digit number)
43532731752814990740…77417504791393282239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.706 Γ— 10⁹⁷(98-digit number)
87065463505629981480…54835009582786564479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.741 Γ— 10⁹⁸(99-digit number)
17413092701125996296…09670019165573128959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.482 Γ— 10⁹⁸(99-digit number)
34826185402251992592…19340038331146257919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.965 Γ— 10⁹⁸(99-digit number)
69652370804503985184…38680076662292515839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.393 Γ— 10⁹⁹(100-digit number)
13930474160900797036…77360153324585031679
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 404984

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 06f10c7db4673986e2752c281dc207e21b6d22a26e3a2f0371fa4cec4ff16562

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 #404,984 on Chainz β†—
Circulating Supply:57,637,842 XPMΒ·at block #6,799,224 Β· updates every 60s
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