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Block #274,436

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/26/2013, 7:14:58 AM Β· Difficulty 9.9574 Β· 6,551,678 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cffffe44aaa8e6ff2387953a5aa55d9d9e837d2b500ca151924ace77b171253b
View on Chainz β†—

Height

#274,436

Difficulty

9.957417

Transactions

2

Size

470 B

Version

2

Bits

09f51950

Nonce

76,350

Timestamp

11/26/2013, 7:14:58 AM

Confirmations

6,551,678

Merkle Root

adff872c9b71fc957d10d551b91274a1cabe8ee28e07a4919b8a2aba071ce207
Transactions (2)
Coinbase0b26175b96ea71…d25d122592305b
1 in β†’ 1 out10.0800 XPM109 B
AJZbHY79…XjUsVhdQ
57d47058c96bb7…4a2ea04eb7dc78
2 in β†’ 1 out20.1300 XPM271 B
AKN6pNCw…MeATKM2o
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.

1.107 Γ— 10⁹⁴(95-digit number)
11070100281516996770…72696297009750575290
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
1.107 Γ— 10⁹⁴(95-digit number)
11070100281516996770…72696297009750575289
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.214 Γ— 10⁹⁴(95-digit number)
22140200563033993541…45392594019501150579
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.428 Γ— 10⁹⁴(95-digit number)
44280401126067987082…90785188039002301159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.856 Γ— 10⁹⁴(95-digit number)
88560802252135974165…81570376078004602319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.771 Γ— 10⁹⁡(96-digit number)
17712160450427194833…63140752156009204639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.542 Γ— 10⁹⁡(96-digit number)
35424320900854389666…26281504312018409279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.084 Γ— 10⁹⁡(96-digit number)
70848641801708779332…52563008624036818559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.416 Γ— 10⁹⁢(97-digit number)
14169728360341755866…05126017248073637119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.833 Γ— 10⁹⁢(97-digit number)
28339456720683511732…10252034496147274239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.667 Γ— 10⁹⁢(97-digit number)
56678913441367023465…20504068992294548479
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 274436

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 cffffe44aaa8e6ff2387953a5aa55d9d9e837d2b500ca151924ace77b171253b

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 #274,436 on Chainz β†—
Circulating Supply:57,853,037 XPMΒ·at block #6,826,113 Β· updates every 60s
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