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Block #318,676

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/18/2013, 12:47:57 PM Β· Difficulty 10.1608 Β· 6,497,461 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ab61f2bc10296da548c12bb83ec18bdf4616a0a4d52af8ab165fa62ea3fcae76
View on Chainz β†—

Height

#318,676

Difficulty

10.160782

Transactions

1

Size

210 B

Version

2

Bits

0a292908

Nonce

102,732

Timestamp

12/18/2013, 12:47:57 PM

Confirmations

6,497,461

Merkle Root

ea3cb8503a5c5b094b2dbad93f061db0dc9f59eff0b53b130f5d5bb664c866b6
Transactions (1)
Coinbaseea3cb8503a5c5b…5d5bb664c866b6
1 in β†’ 1 out9.6700 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.

8.015 Γ— 10¹⁰⁴(105-digit number)
80155198435283383219…60164656995063690560
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
8.015 Γ— 10¹⁰⁴(105-digit number)
80155198435283383219…60164656995063690559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.603 Γ— 10¹⁰⁡(106-digit number)
16031039687056676643…20329313990127381119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.206 Γ— 10¹⁰⁡(106-digit number)
32062079374113353287…40658627980254762239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.412 Γ— 10¹⁰⁡(106-digit number)
64124158748226706575…81317255960509524479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.282 Γ— 10¹⁰⁢(107-digit number)
12824831749645341315…62634511921019048959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.564 Γ— 10¹⁰⁢(107-digit number)
25649663499290682630…25269023842038097919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.129 Γ— 10¹⁰⁢(107-digit number)
51299326998581365260…50538047684076195839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.025 Γ— 10¹⁰⁷(108-digit number)
10259865399716273052…01076095368152391679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.051 Γ— 10¹⁰⁷(108-digit number)
20519730799432546104…02152190736304783359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.103 Γ— 10¹⁰⁷(108-digit number)
41039461598865092208…04304381472609566719
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 318676

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 ab61f2bc10296da548c12bb83ec18bdf4616a0a4d52af8ab165fa62ea3fcae76

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 #318,676 on Chainz β†—
Circulating Supply:57,773,223 XPMΒ·at block #6,816,136 Β· updates every 60s
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