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Block #406,681

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/16/2014, 10:12:25 AM Β· Difficulty 10.4339 Β· 6,396,911 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
77d2fd1fe86c5e587e903c08a3283f1f2d0bfa73c2e085bd5a7ea7eaae80b726
View on Chainz β†—

Height

#406,681

Difficulty

10.433870

Transactions

1

Size

201 B

Version

2

Bits

0a6f1223

Nonce

316,636

Timestamp

2/16/2014, 10:12:25 AM

Confirmations

6,396,911

Merkle Root

c4586a1b675b43f986a2dd0d73e8183e42b2fbc82092020491967f6357d8fcac
Transactions (1)
Coinbasec4586a1b675b43…967f6357d8fcac
1 in β†’ 1 out9.1700 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.

1.208 Γ— 10⁹⁸(99-digit number)
12085048986970486902…45340748485822844800
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
1.208 Γ— 10⁹⁸(99-digit number)
12085048986970486902…45340748485822844799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.417 Γ— 10⁹⁸(99-digit number)
24170097973940973805…90681496971645689599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.834 Γ— 10⁹⁸(99-digit number)
48340195947881947610…81362993943291379199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.668 Γ— 10⁹⁸(99-digit number)
96680391895763895220…62725987886582758399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.933 Γ— 10⁹⁹(100-digit number)
19336078379152779044…25451975773165516799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.867 Γ— 10⁹⁹(100-digit number)
38672156758305558088…50903951546331033599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.734 Γ— 10⁹⁹(100-digit number)
77344313516611116176…01807903092662067199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.546 Γ— 10¹⁰⁰(101-digit number)
15468862703322223235…03615806185324134399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.093 Γ— 10¹⁰⁰(101-digit number)
30937725406644446470…07231612370648268799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.187 Γ— 10¹⁰⁰(101-digit number)
61875450813288892941…14463224741296537599
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 406681

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 77d2fd1fe86c5e587e903c08a3283f1f2d0bfa73c2e085bd5a7ea7eaae80b726

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 #406,681 on Chainz β†—
Circulating Supply:57,672,773 XPMΒ·at block #6,803,591 Β· updates every 60s
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