XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #104,847

Block #104,847

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2013, 6:08:16 AM Β· Difficulty 9.5679 Β· 6,695,986 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
74ee7ffa3cb740643ab7f7101c3d8be81e2be001161ed20b6ebd6c016ab1ecc9
View on Chainz β†—

Height

#104,847

Difficulty

9.567920

Transactions

1

Size

199 B

Version

2

Bits

0991632f

Nonce

133,595

Timestamp

8/8/2013, 6:08:16 AM

Confirmations

6,695,986

Merkle Root

2b52c8d792927f2fb834a9ff9d4dfd008eb6a3b423ba1438f83718103a09c16d
Transactions (1)
Coinbase2b52c8d792927f…3718103a09c16d
1 in β†’ 1 out10.9100 XPM109 B
AezMwyLP…rTg7Eyfk
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.

1.241 Γ— 10⁹⁡(96-digit number)
12411857728535366748…71987791194005719600
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
1.241 Γ— 10⁹⁡(96-digit number)
12411857728535366748…71987791194005719599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.482 Γ— 10⁹⁡(96-digit number)
24823715457070733497…43975582388011439199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.964 Γ— 10⁹⁡(96-digit number)
49647430914141466995…87951164776022878399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.929 Γ— 10⁹⁡(96-digit number)
99294861828282933990…75902329552045756799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.985 Γ— 10⁹⁢(97-digit number)
19858972365656586798…51804659104091513599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.971 Γ— 10⁹⁢(97-digit number)
39717944731313173596…03609318208183027199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.943 Γ— 10⁹⁢(97-digit number)
79435889462626347192…07218636416366054399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.588 Γ— 10⁹⁷(98-digit number)
15887177892525269438…14437272832732108799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.177 Γ— 10⁹⁷(98-digit number)
31774355785050538877…28874545665464217599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 104847

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 74ee7ffa3cb740643ab7f7101c3d8be81e2be001161ed20b6ebd6c016ab1ecc9

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 #104,847 on Chainz β†—
Circulating Supply:57,650,722 XPMΒ·at block #6,800,832 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK