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Home/Chain Registry/Block #839,824

Block #839,824

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/4/2014, 5:00:06 PM Β· Difficulty 10.9745 Β· 6,001,951 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
35846076145f0941530afc7f298afebbc551e984a9e466212a655c1db05d56ed
View on Chainz β†—

Height

#839,824

Difficulty

10.974450

Transactions

2

Size

431 B

Version

2

Bits

0af9758f

Nonce

553,462,014

Timestamp

12/4/2014, 5:00:06 PM

Confirmations

6,001,951

Merkle Root

4a128a1007588445aed4402aa8382d53962d644d5003a04becb9569e6cfb7283
Transactions (2)
Coinbase9af78070877454…2ac0c354335f4d
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
ee3b12e708370c…760d6487a362fc
1 in β†’ 2 out0.1564 XPM225 B
AHP9TLMS…FACrYF4dAb1sc7zk…D5DV9hyu
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.

6.551 Γ— 10⁹⁴(95-digit number)
65513460980958025082…24773715857181652480
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
6.551 Γ— 10⁹⁴(95-digit number)
65513460980958025082…24773715857181652479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.310 Γ— 10⁹⁡(96-digit number)
13102692196191605016…49547431714363304959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.620 Γ— 10⁹⁡(96-digit number)
26205384392383210033…99094863428726609919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.241 Γ— 10⁹⁡(96-digit number)
52410768784766420066…98189726857453219839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.048 Γ— 10⁹⁢(97-digit number)
10482153756953284013…96379453714906439679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.096 Γ— 10⁹⁢(97-digit number)
20964307513906568026…92758907429812879359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.192 Γ— 10⁹⁢(97-digit number)
41928615027813136052…85517814859625758719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.385 Γ— 10⁹⁢(97-digit number)
83857230055626272105…71035629719251517439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.677 Γ— 10⁹⁷(98-digit number)
16771446011125254421…42071259438503034879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.354 Γ— 10⁹⁷(98-digit number)
33542892022250508842…84142518877006069759
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 839824

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 35846076145f0941530afc7f298afebbc551e984a9e466212a655c1db05d56ed

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 #839,824 on Chainz β†—
Circulating Supply:57,978,577 XPMΒ·at block #6,841,774 Β· updates every 60s
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