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Block #338,069

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/1/2014, 4:21:15 AM Β· Difficulty 10.1233 Β· 6,478,229 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
de4915add37e9299fabb687f9b770a22b4d15aa737b5e62e514b8fdcc905ab55
View on Chainz β†—

Height

#338,069

Difficulty

10.123283

Transactions

1

Size

206 B

Version

2

Bits

0a1f8f76

Nonce

177,919

Timestamp

1/1/2014, 4:21:15 AM

Confirmations

6,478,229

Merkle Root

209d099c38ad2ab6ce30fd3a2f267fca138f46955a71f21bf424ffbf6b007500
Transactions (1)
Coinbase209d099c38ad2a…24ffbf6b007500
1 in β†’ 1 out9.7400 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.

7.587 Γ— 10⁹⁡(96-digit number)
75870283021425873445…65816206065270188800
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
7.587 Γ— 10⁹⁡(96-digit number)
75870283021425873445…65816206065270188799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.517 Γ— 10⁹⁢(97-digit number)
15174056604285174689…31632412130540377599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.034 Γ— 10⁹⁢(97-digit number)
30348113208570349378…63264824261080755199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.069 Γ— 10⁹⁢(97-digit number)
60696226417140698756…26529648522161510399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.213 Γ— 10⁹⁷(98-digit number)
12139245283428139751…53059297044323020799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.427 Γ— 10⁹⁷(98-digit number)
24278490566856279502…06118594088646041599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.855 Γ— 10⁹⁷(98-digit number)
48556981133712559004…12237188177292083199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.711 Γ— 10⁹⁷(98-digit number)
97113962267425118009…24474376354584166399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.942 Γ— 10⁹⁸(99-digit number)
19422792453485023601…48948752709168332799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.884 Γ— 10⁹⁸(99-digit number)
38845584906970047203…97897505418336665599
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 338069

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 de4915add37e9299fabb687f9b770a22b4d15aa737b5e62e514b8fdcc905ab55

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 #338,069 on Chainz β†—
Circulating Supply:57,774,503 XPMΒ·at block #6,816,297 Β· updates every 60s
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