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Block #922,646

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/4/2015, 3:39:53 PM Β· Difficulty 10.9149 Β· 5,902,065 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5de3d2cc19ab41db65b03350beaac628153f7139cbce3dcd2cc89250228bc531
View on Chainz β†—

Height

#922,646

Difficulty

10.914860

Transactions

1

Size

206 B

Version

2

Bits

0aea3440

Nonce

931,565,295

Timestamp

2/4/2015, 3:39:53 PM

Confirmations

5,902,065

Merkle Root

81d5bbc03eef776c2fbd86d968bf7a7f64b8ab7ad2f6cc45c919f74f8853701d
Transactions (1)
Coinbase81d5bbc03eef77…19f74f8853701d
1 in β†’ 1 out8.3800 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.

2.565 Γ— 10⁹⁡(96-digit number)
25658249953140006692…54416278565205038980
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
2.565 Γ— 10⁹⁡(96-digit number)
25658249953140006692…54416278565205038981
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.131 Γ— 10⁹⁡(96-digit number)
51316499906280013385…08832557130410077961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.026 Γ— 10⁹⁢(97-digit number)
10263299981256002677…17665114260820155921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.052 Γ— 10⁹⁢(97-digit number)
20526599962512005354…35330228521640311841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.105 Γ— 10⁹⁢(97-digit number)
41053199925024010708…70660457043280623681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.210 Γ— 10⁹⁢(97-digit number)
82106399850048021416…41320914086561247361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.642 Γ— 10⁹⁷(98-digit number)
16421279970009604283…82641828173122494721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.284 Γ— 10⁹⁷(98-digit number)
32842559940019208566…65283656346244989441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.568 Γ— 10⁹⁷(98-digit number)
65685119880038417133…30567312692489978881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.313 Γ— 10⁹⁸(99-digit number)
13137023976007683426…61134625384979957761
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 922646

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 5de3d2cc19ab41db65b03350beaac628153f7139cbce3dcd2cc89250228bc531

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 #922,646 on Chainz β†—
Circulating Supply:57,841,754 XPMΒ·at block #6,824,710 Β· updates every 60s
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