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Block #410,565

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/19/2014, 3:59:30 AM Β· Difficulty 10.4286 Β· 6,416,383 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
00fe729552109b3ce704e36af3d5c303dceb0c6bbc1ada032a20cb4d4648669a
View on Chainz β†—

Height

#410,565

Difficulty

10.428617

Transactions

1

Size

207 B

Version

2

Bits

0a6db9d5

Nonce

15,549

Timestamp

2/19/2014, 3:59:30 AM

Confirmations

6,416,383

Merkle Root

6b67f531dc92eaa7e1286a531d110f6256b328eecd9b9873b8dbf50c6886bca1
Transactions (1)
Coinbase6b67f531dc92ea…dbf50c6886bca1
1 in β†’ 1 out9.1800 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.

1.133 Γ— 10⁹⁷(98-digit number)
11332982724430591813…06830269824615137180
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
1.133 Γ— 10⁹⁷(98-digit number)
11332982724430591813…06830269824615137181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.266 Γ— 10⁹⁷(98-digit number)
22665965448861183627…13660539649230274361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.533 Γ— 10⁹⁷(98-digit number)
45331930897722367254…27321079298460548721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.066 Γ— 10⁹⁷(98-digit number)
90663861795444734509…54642158596921097441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.813 Γ— 10⁹⁸(99-digit number)
18132772359088946901…09284317193842194881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.626 Γ— 10⁹⁸(99-digit number)
36265544718177893803…18568634387684389761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.253 Γ— 10⁹⁸(99-digit number)
72531089436355787607…37137268775368779521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.450 Γ— 10⁹⁹(100-digit number)
14506217887271157521…74274537550737559041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.901 Γ— 10⁹⁹(100-digit number)
29012435774542315042…48549075101475118081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.802 Γ— 10⁹⁹(100-digit number)
58024871549084630085…97098150202950236161
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 410565

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 00fe729552109b3ce704e36af3d5c303dceb0c6bbc1ada032a20cb4d4648669a

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 #410,565 on Chainz β†—
Circulating Supply:57,859,759 XPMΒ·at block #6,826,947 Β· updates every 60s
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