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Block #275,316

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/26/2013, 3:57:59 PM Β· Difficulty 9.9604 Β· 6,520,098 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7214eca0d02c623048d7dfdee8fb39c8ff32ee7769a8c5ad22f8ad50d2eba61c
View on Chainz β†—

Height

#275,316

Difficulty

9.960376

Transactions

1

Size

201 B

Version

2

Bits

09f5db2f

Nonce

420,089

Timestamp

11/26/2013, 3:57:59 PM

Confirmations

6,520,098

Merkle Root

f102308c9833bf6f708b5c5e31087143133d67d72c7ed6665fa0e9f95aa9dcf6
Transactions (1)
Coinbasef102308c9833bf…a0e9f95aa9dcf6
1 in β†’ 1 out10.0600 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.270 Γ— 10⁹⁷(98-digit number)
22700385276361152733…68143266797653995520
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
2.270 Γ— 10⁹⁷(98-digit number)
22700385276361152733…68143266797653995519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.540 Γ— 10⁹⁷(98-digit number)
45400770552722305466…36286533595307991039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.080 Γ— 10⁹⁷(98-digit number)
90801541105444610933…72573067190615982079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.816 Γ— 10⁹⁸(99-digit number)
18160308221088922186…45146134381231964159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.632 Γ— 10⁹⁸(99-digit number)
36320616442177844373…90292268762463928319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.264 Γ— 10⁹⁸(99-digit number)
72641232884355688746…80584537524927856639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.452 Γ— 10⁹⁹(100-digit number)
14528246576871137749…61169075049855713279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.905 Γ— 10⁹⁹(100-digit number)
29056493153742275498…22338150099711426559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.811 Γ— 10⁹⁹(100-digit number)
58112986307484550997…44676300199422853119
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 275316

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 7214eca0d02c623048d7dfdee8fb39c8ff32ee7769a8c5ad22f8ad50d2eba61c

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 #275,316 on Chainz β†—
Circulating Supply:57,607,372 XPMΒ·at block #6,795,413 Β· updates every 60s
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