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Block #719,816

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/14/2014, 2:56:14 AM Β· Difficulty 10.9509 Β· 6,106,864 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c9e18d2ec5bd0b8580f9de6469e944e24681d12da3469b8684d018bfb6be711c
View on Chainz β†—

Height

#719,816

Difficulty

10.950876

Transactions

1

Size

207 B

Version

2

Bits

0af36ca4

Nonce

2,279,481,938

Timestamp

9/14/2014, 2:56:14 AM

Confirmations

6,106,864

Merkle Root

1f53c5ea446cd000e75140c313d94926d4150928c33a47b57ba03bb20d8082c4
Transactions (1)
Coinbase1f53c5ea446cd0…a03bb20d8082c4
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.254 Γ— 10⁹⁢(97-digit number)
32544694025822440526…47611316838842810880
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
3.254 Γ— 10⁹⁢(97-digit number)
32544694025822440526…47611316838842810881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.508 Γ— 10⁹⁢(97-digit number)
65089388051644881052…95222633677685621761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.301 Γ— 10⁹⁷(98-digit number)
13017877610328976210…90445267355371243521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.603 Γ— 10⁹⁷(98-digit number)
26035755220657952421…80890534710742487041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.207 Γ— 10⁹⁷(98-digit number)
52071510441315904842…61781069421484974081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.041 Γ— 10⁹⁸(99-digit number)
10414302088263180968…23562138842969948161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.082 Γ— 10⁹⁸(99-digit number)
20828604176526361936…47124277685939896321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.165 Γ— 10⁹⁸(99-digit number)
41657208353052723873…94248555371879792641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.331 Γ— 10⁹⁸(99-digit number)
83314416706105447747…88497110743759585281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.666 Γ— 10⁹⁹(100-digit number)
16662883341221089549…76994221487519170561
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 719816

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 c9e18d2ec5bd0b8580f9de6469e944e24681d12da3469b8684d018bfb6be711c

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 #719,816 on Chainz β†—
Circulating Supply:57,857,589 XPMΒ·at block #6,826,679 Β· updates every 60s
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