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Home/Chain Registry/Block #865,231

Block #865,231

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/23/2014, 6:41:34 PM Β· Difficulty 10.9626 Β· 5,946,864 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
37c4ee9d12dfce6ad3377db6e27fffab845ad205b06b7294bc465575d479d8b6
View on Chainz β†—

Height

#865,231

Difficulty

10.962570

Transactions

2

Size

615 B

Version

2

Bits

0af66b00

Nonce

2,715,137,027

Timestamp

12/23/2014, 6:41:34 PM

Confirmations

5,946,864

Merkle Root

1b688a7505e3b64974a0e0216dc8f65231c6cc16d94ddef3b13f1240b061d10a
Transactions (2)
Coinbase92a0c524023aa5…e220503a84b974
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
7e75c81c687be5…1eb38e14d356ce
2 in β†’ 3 out1.0970 XPM409 B
AJ4WTVZa…GDXAy1UyAeUEX7rM…ei71Di56ALLWB6Pb…sMY8TkKC
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.

2.712 Γ— 10⁹⁡(96-digit number)
27121073952306218684…65051551520371983840
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
2.712 Γ— 10⁹⁡(96-digit number)
27121073952306218684…65051551520371983839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.424 Γ— 10⁹⁡(96-digit number)
54242147904612437368…30103103040743967679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.084 Γ— 10⁹⁢(97-digit number)
10848429580922487473…60206206081487935359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.169 Γ— 10⁹⁢(97-digit number)
21696859161844974947…20412412162975870719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.339 Γ— 10⁹⁢(97-digit number)
43393718323689949894…40824824325951741439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.678 Γ— 10⁹⁢(97-digit number)
86787436647379899789…81649648651903482879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.735 Γ— 10⁹⁷(98-digit number)
17357487329475979957…63299297303806965759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.471 Γ— 10⁹⁷(98-digit number)
34714974658951959915…26598594607613931519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.942 Γ— 10⁹⁷(98-digit number)
69429949317903919831…53197189215227863039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.388 Γ— 10⁹⁸(99-digit number)
13885989863580783966…06394378430455726079
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 865231

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 37c4ee9d12dfce6ad3377db6e27fffab845ad205b06b7294bc465575d479d8b6

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 #865,231 on Chainz β†—
Circulating Supply:57,740,865 XPMΒ·at block #6,812,094 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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