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Block #342,596

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/4/2014, 4:39:03 AM Β· Difficulty 10.1568 Β· 6,472,493 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
18daf1d70872bf7d11ca3a338917f3c32c400c5d866206d7eff7fe149feda1dc
View on Chainz β†—

Height

#342,596

Difficulty

10.156832

Transactions

1

Size

207 B

Version

2

Bits

0a282629

Nonce

285,212,750

Timestamp

1/4/2014, 4:39:03 AM

Confirmations

6,472,493

Merkle Root

069c2c2f20d302802f75261305d538a3f77aee7e5a6acdf8b7d59d09d77696f4
Transactions (1)
Coinbase069c2c2f20d302…d59d09d77696f4
1 in β†’ 1 out9.6800 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.

5.307 Γ— 10⁹⁢(97-digit number)
53074215185439501312…12602458152469360000
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
5.307 Γ— 10⁹⁢(97-digit number)
53074215185439501312…12602458152469359999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.061 Γ— 10⁹⁷(98-digit number)
10614843037087900262…25204916304938719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.122 Γ— 10⁹⁷(98-digit number)
21229686074175800524…50409832609877439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.245 Γ— 10⁹⁷(98-digit number)
42459372148351601049…00819665219754879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.491 Γ— 10⁹⁷(98-digit number)
84918744296703202099…01639330439509759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.698 Γ— 10⁹⁸(99-digit number)
16983748859340640419…03278660879019519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.396 Γ— 10⁹⁸(99-digit number)
33967497718681280839…06557321758039039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.793 Γ— 10⁹⁸(99-digit number)
67934995437362561679…13114643516078079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.358 Γ— 10⁹⁹(100-digit number)
13586999087472512335…26229287032156159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.717 Γ— 10⁹⁹(100-digit number)
27173998174945024671…52458574064312319999
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 342596

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 18daf1d70872bf7d11ca3a338917f3c32c400c5d866206d7eff7fe149feda1dc

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 #342,596 on Chainz β†—
Circulating Supply:57,764,800 XPMΒ·at block #6,815,088 Β· updates every 60s
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