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Block #49,647

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/15/2013, 9:23:55 PM Β· Difficulty 8.8688 Β· 6,745,767 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
751f83af9d94a0e8f33331d1f9c05b3d6d9cc4ed3dfd65d1e39ce8791ed24b15
View on Chainz β†—

Height

#49,647

Difficulty

8.868810

Transactions

1

Size

205 B

Version

2

Bits

08de6a4d

Nonce

11

Timestamp

7/15/2013, 9:23:55 PM

Confirmations

6,745,767

Merkle Root

a50bfbe299b50c043eb9b76db19606c0885689e69d9748cfbfb9a00172110086
Transactions (1)
Coinbasea50bfbe299b50c…b9a00172110086
1 in β†’ 1 out12.7000 XPM110 B
AJuLD3aS…KEXNe2ke
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.

1.904 Γ— 10¹⁰⁷(108-digit number)
19048520976811623556…49057356658219255510
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
1.904 Γ— 10¹⁰⁷(108-digit number)
19048520976811623556…49057356658219255509
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.809 Γ— 10¹⁰⁷(108-digit number)
38097041953623247113…98114713316438511019
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.619 Γ— 10¹⁰⁷(108-digit number)
76194083907246494227…96229426632877022039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.523 Γ— 10¹⁰⁸(109-digit number)
15238816781449298845…92458853265754044079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.047 Γ— 10¹⁰⁸(109-digit number)
30477633562898597691…84917706531508088159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.095 Γ— 10¹⁰⁸(109-digit number)
60955267125797195382…69835413063016176319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.219 Γ— 10¹⁰⁹(110-digit number)
12191053425159439076…39670826126032352639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.438 Γ— 10¹⁰⁹(110-digit number)
24382106850318878152…79341652252064705279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.876 Γ— 10¹⁰⁹(110-digit number)
48764213700637756305…58683304504129410559
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 49647

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 751f83af9d94a0e8f33331d1f9c05b3d6d9cc4ed3dfd65d1e39ce8791ed24b15

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 #49,647 on Chainz β†—
Circulating Supply:57,607,372 XPMΒ·at block #6,795,413 Β· updates every 60s
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