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Block #318,406

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/18/2013, 8:09:44 AM Β· Difficulty 10.1617 Β· 6,477,531 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c72e1c6309ea356f91f89612f01fc6d209584237079e7bd7de9afbc4c7ea3cf2
View on Chainz β†—

Height

#318,406

Difficulty

10.161678

Transactions

1

Size

202 B

Version

2

Bits

0a2963c2

Nonce

18,627

Timestamp

12/18/2013, 8:09:44 AM

Confirmations

6,477,531

Merkle Root

ec66215ae305d57ddc1f5a350494ee49cec1fc28cd615746d49795db91ad53ec
Transactions (1)
Coinbaseec66215ae305d5…9795db91ad53ec
1 in β†’ 1 out9.6700 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.

1.301 Γ— 10¹⁰⁰(101-digit number)
13010861623280428831…14625695722906559740
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
1.301 Γ— 10¹⁰⁰(101-digit number)
13010861623280428831…14625695722906559739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.602 Γ— 10¹⁰⁰(101-digit number)
26021723246560857662…29251391445813119479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.204 Γ— 10¹⁰⁰(101-digit number)
52043446493121715325…58502782891626238959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.040 Γ— 10¹⁰¹(102-digit number)
10408689298624343065…17005565783252477919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.081 Γ— 10¹⁰¹(102-digit number)
20817378597248686130…34011131566504955839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.163 Γ— 10¹⁰¹(102-digit number)
41634757194497372260…68022263133009911679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.326 Γ— 10¹⁰¹(102-digit number)
83269514388994744520…36044526266019823359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.665 Γ— 10¹⁰²(103-digit number)
16653902877798948904…72089052532039646719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.330 Γ— 10¹⁰²(103-digit number)
33307805755597897808…44178105064079293439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.661 Γ— 10¹⁰²(103-digit number)
66615611511195795616…88356210128158586879
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 318406

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 c72e1c6309ea356f91f89612f01fc6d209584237079e7bd7de9afbc4c7ea3cf2

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 #318,406 on Chainz β†—
Circulating Supply:57,611,585 XPMΒ·at block #6,795,936 Β· updates every 60s
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