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Block #346,893

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/6/2014, 8:07:40 PM Β· Difficulty 10.2355 Β· 6,454,357 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
00a6ceb471fd2b64794a7ce3a47a1193a042e5742f55e307f71f292936e3e382
View on Chainz β†—

Height

#346,893

Difficulty

10.235472

Transactions

1

Size

207 B

Version

2

Bits

0a3c47ea

Nonce

13,827

Timestamp

1/6/2014, 8:07:40 PM

Confirmations

6,454,357

Merkle Root

066e488b8e21d63d2fc3fbe967d725e16dcfd3a4ec5c6b1be644f4b383c4f98e
Transactions (1)
Coinbase066e488b8e21d6…44f4b383c4f98e
1 in β†’ 1 out9.5300 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.

1.361 Γ— 10⁹⁷(98-digit number)
13618123861393689968…99955299210980397140
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
1.361 Γ— 10⁹⁷(98-digit number)
13618123861393689968…99955299210980397139
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.723 Γ— 10⁹⁷(98-digit number)
27236247722787379936…99910598421960794279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.447 Γ— 10⁹⁷(98-digit number)
54472495445574759873…99821196843921588559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.089 Γ— 10⁹⁸(99-digit number)
10894499089114951974…99642393687843177119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.178 Γ— 10⁹⁸(99-digit number)
21788998178229903949…99284787375686354239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.357 Γ— 10⁹⁸(99-digit number)
43577996356459807898…98569574751372708479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.715 Γ— 10⁹⁸(99-digit number)
87155992712919615797…97139149502745416959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.743 Γ— 10⁹⁹(100-digit number)
17431198542583923159…94278299005490833919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.486 Γ— 10⁹⁹(100-digit number)
34862397085167846318…88556598010981667839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.972 Γ— 10⁹⁹(100-digit number)
69724794170335692637…77113196021963335679
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 346893

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 00a6ceb471fd2b64794a7ce3a47a1193a042e5742f55e307f71f292936e3e382

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 #346,893 on Chainz β†—
Circulating Supply:57,654,068 XPMΒ·at block #6,801,249 Β· updates every 60s
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