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Block #348,863

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/8/2014, 1:25:55 AM Β· Difficulty 10.2671 Β· 6,446,649 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
77b056dac39b173b9afeda9fcaaa87aa893e006c20cdb3e189a0a2115c9cce11
View on Chainz β†—

Height

#348,863

Difficulty

10.267139

Transactions

1

Size

210 B

Version

2

Bits

0a446332

Nonce

34,368

Timestamp

1/8/2014, 1:25:55 AM

Confirmations

6,446,649

Merkle Root

68cb9398bf0c83330a4fe18f8df46248e3660f989ffba9f4f2682708a5ff7ab6
Transactions (1)
Coinbase68cb9398bf0c83…682708a5ff7ab6
1 in β†’ 1 out9.4700 XPM116 B
AbwWkWZt…kawDhufa
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.

2.630 Γ— 10¹⁰⁡(106-digit number)
26305829018248721405…22825244372204688480
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
2.630 Γ— 10¹⁰⁡(106-digit number)
26305829018248721405…22825244372204688479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.261 Γ— 10¹⁰⁡(106-digit number)
52611658036497442811…45650488744409376959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.052 Γ— 10¹⁰⁢(107-digit number)
10522331607299488562…91300977488818753919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.104 Γ— 10¹⁰⁢(107-digit number)
21044663214598977124…82601954977637507839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.208 Γ— 10¹⁰⁢(107-digit number)
42089326429197954249…65203909955275015679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.417 Γ— 10¹⁰⁢(107-digit number)
84178652858395908499…30407819910550031359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.683 Γ— 10¹⁰⁷(108-digit number)
16835730571679181699…60815639821100062719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.367 Γ— 10¹⁰⁷(108-digit number)
33671461143358363399…21631279642200125439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.734 Γ— 10¹⁰⁷(108-digit number)
67342922286716726799…43262559284400250879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.346 Γ— 10¹⁰⁸(109-digit number)
13468584457343345359…86525118568800501759
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 348863

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 77b056dac39b173b9afeda9fcaaa87aa893e006c20cdb3e189a0a2115c9cce11

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 #348,863 on Chainz β†—
Circulating Supply:57,608,159 XPMΒ·at block #6,795,511 Β· updates every 60s
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