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Block #293,755

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/4/2013, 12:11:25 PM Β· Difficulty 9.9907 Β· 6,502,016 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c32b9236b52546abb94bd57a983172e908c68abaee745d1ecdcf46118a8a2a2c
View on Chainz β†—

Height

#293,755

Difficulty

9.990744

Transactions

1

Size

209 B

Version

2

Bits

09fda16d

Nonce

779

Timestamp

12/4/2013, 12:11:25 PM

Confirmations

6,502,016

Merkle Root

031edf2bc807909292ad10ea508ddef6b0c91bbc93744ff100a283f4d0858728
Transactions (1)
Coinbase031edf2bc80790…a283f4d0858728
1 in β†’ 1 out10.0000 XPM116 B
AcLBm5Z9…S683d7c3
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.

4.778 Γ— 10¹⁰²(103-digit number)
47786567018977681576…24085056552142110720
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
4.778 Γ— 10¹⁰²(103-digit number)
47786567018977681576…24085056552142110719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.557 Γ— 10¹⁰²(103-digit number)
95573134037955363153…48170113104284221439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.911 Γ— 10¹⁰³(104-digit number)
19114626807591072630…96340226208568442879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.822 Γ— 10¹⁰³(104-digit number)
38229253615182145261…92680452417136885759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.645 Γ— 10¹⁰³(104-digit number)
76458507230364290523…85360904834273771519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.529 Γ— 10¹⁰⁴(105-digit number)
15291701446072858104…70721809668547543039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.058 Γ— 10¹⁰⁴(105-digit number)
30583402892145716209…41443619337095086079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.116 Γ— 10¹⁰⁴(105-digit number)
61166805784291432418…82887238674190172159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.223 Γ— 10¹⁰⁡(106-digit number)
12233361156858286483…65774477348380344319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.446 Γ— 10¹⁰⁡(106-digit number)
24466722313716572967…31548954696760688639
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 293755

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 c32b9236b52546abb94bd57a983172e908c68abaee745d1ecdcf46118a8a2a2c

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 #293,755 on Chainz β†—
Circulating Supply:57,610,251 XPMΒ·at block #6,795,770 Β· updates every 60s
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