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Block #416,987

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/23/2014, 8:06:30 PM Β· Difficulty 10.3958 Β· 6,407,998 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ee8a34ae2ce581a20ec36b96b029d00b9ac0c128fd911366f3809f62a8f761aa
View on Chainz β†—

Height

#416,987

Difficulty

10.395764

Transactions

1

Size

935 B

Version

2

Bits

0a6550ce

Nonce

8,259

Timestamp

2/23/2014, 8:06:30 PM

Confirmations

6,407,998

Merkle Root

3819da21576e59f647262886ef43135d8c3b326b87f129e965a6eeef312b8197
Transactions (1)
Coinbase3819da21576e59…a6eeef312b8197
1 in β†’ 23 out9.2400 XPM845 B
AQwRN8bE…V8PsTcY9AP9eJ2CZ…eYfb95GNANNg88pG…ppn21sTeAac9Hjdg…P4ktypc3AJLB8H7s…MRD4s5wA
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.

2.270 Γ— 10⁹⁴(95-digit number)
22702043119304576354…37004494649163776000
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.270 Γ— 10⁹⁴(95-digit number)
22702043119304576354…37004494649163776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.540 Γ— 10⁹⁴(95-digit number)
45404086238609152708…74008989298327552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.080 Γ— 10⁹⁴(95-digit number)
90808172477218305417…48017978596655104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.816 Γ— 10⁹⁡(96-digit number)
18161634495443661083…96035957193310208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.632 Γ— 10⁹⁡(96-digit number)
36323268990887322167…92071914386620416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.264 Γ— 10⁹⁡(96-digit number)
72646537981774644334…84143828773240832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.452 Γ— 10⁹⁢(97-digit number)
14529307596354928866…68287657546481664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.905 Γ— 10⁹⁢(97-digit number)
29058615192709857733…36575315092963328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.811 Γ— 10⁹⁢(97-digit number)
58117230385419715467…73150630185926656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.162 Γ— 10⁹⁷(98-digit number)
11623446077083943093…46301260371853312001
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 416987

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 ee8a34ae2ce581a20ec36b96b029d00b9ac0c128fd911366f3809f62a8f761aa

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 #416,987 on Chainz β†—
Circulating Supply:57,843,963 XPMΒ·at block #6,824,984 Β· updates every 60s
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