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Block #910,791

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/26/2015, 2:09:39 PM Β· Difficulty 10.9325 Β· 5,901,710 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5bf7fa24aa28353add1115ae926ff94174bcb5cda535470e21263d6fcf9021db
View on Chainz β†—

Height

#910,791

Difficulty

10.932512

Transactions

1

Size

243 B

Version

2

Bits

0aeeb913

Nonce

31,932,079

Timestamp

1/26/2015, 2:09:39 PM

Confirmations

5,901,710

Merkle Root

021c9f6ef298e45c211b51664bc998899d2c9c4fb88943c0c927ceeea47bf9ac
Transactions (1)
Coinbase021c9f6ef298e4…27ceeea47bf9ac
1 in β†’ 2 out8.3500 XPM152 B
AXCWf4C4…4xLm3nT7ALPu3s2c…EJXLjVFh
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.

3.337 Γ— 10⁹⁷(98-digit number)
33374212362707852403…07250664676514483200
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
3.337 Γ— 10⁹⁷(98-digit number)
33374212362707852403…07250664676514483199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.674 Γ— 10⁹⁷(98-digit number)
66748424725415704806…14501329353028966399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.334 Γ— 10⁹⁸(99-digit number)
13349684945083140961…29002658706057932799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.669 Γ— 10⁹⁸(99-digit number)
26699369890166281922…58005317412115865599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.339 Γ— 10⁹⁸(99-digit number)
53398739780332563845…16010634824231731199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.067 Γ— 10⁹⁹(100-digit number)
10679747956066512769…32021269648463462399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.135 Γ— 10⁹⁹(100-digit number)
21359495912133025538…64042539296926924799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.271 Γ— 10⁹⁹(100-digit number)
42718991824266051076…28085078593853849599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.543 Γ— 10⁹⁹(100-digit number)
85437983648532102152…56170157187707699199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.708 Γ— 10¹⁰⁰(101-digit number)
17087596729706420430…12340314375415398399
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 910791

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 5bf7fa24aa28353add1115ae926ff94174bcb5cda535470e21263d6fcf9021db

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 #910,791 on Chainz β†—
Circulating Supply:57,744,040 XPMΒ·at block #6,812,500 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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