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Block #241,116

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/3/2013, 12:20:13 AM Β· Difficulty 9.9577 Β· 6,557,721 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2b19120d563b80b9adc2635753d676255636e2f60a66236078e5c157bb9705c3
View on Chainz β†—

Height

#241,116

Difficulty

9.957699

Transactions

1

Size

204 B

Version

2

Bits

09f52bc1

Nonce

5

Timestamp

11/3/2013, 12:20:13 AM

Confirmations

6,557,721

Merkle Root

1a654bae807fffb8fdf317e28036ed5540eea30e65efc29e89b5306eedc5f46b
Transactions (1)
Coinbase1a654bae807fff…b5306eedc5f46b
1 in β†’ 1 out10.0700 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.

1.488 Γ— 10⁹⁰(91-digit number)
14882661829611422879…46144696568913327240
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
1.488 Γ— 10⁹⁰(91-digit number)
14882661829611422879…46144696568913327239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.976 Γ— 10⁹⁰(91-digit number)
29765323659222845758…92289393137826654479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.953 Γ— 10⁹⁰(91-digit number)
59530647318445691516…84578786275653308959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.190 Γ— 10⁹¹(92-digit number)
11906129463689138303…69157572551306617919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.381 Γ— 10⁹¹(92-digit number)
23812258927378276606…38315145102613235839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.762 Γ— 10⁹¹(92-digit number)
47624517854756553213…76630290205226471679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.524 Γ— 10⁹¹(92-digit number)
95249035709513106426…53260580410452943359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.904 Γ— 10⁹²(93-digit number)
19049807141902621285…06521160820905886719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.809 Γ— 10⁹²(93-digit number)
38099614283805242570…13042321641811773439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.619 Γ— 10⁹²(93-digit number)
76199228567610485141…26084643283623546879
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 241116

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 2b19120d563b80b9adc2635753d676255636e2f60a66236078e5c157bb9705c3

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 #241,116 on Chainz β†—
Circulating Supply:57,634,727 XPMΒ·at block #6,798,836 Β· updates every 60s
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