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Home/Chain Registry/Block #1,658,292

Block #1,658,292

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/3/2016, 3:21:58 AM Β· Difficulty 10.7944 Β· 5,180,805 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3e3175ddd4ec24002e8bf102c406f0b655763ea6b3e8e3a8f1a466c3a9a35c4f
View on Chainz β†—

Difficulty

10.794355

Transactions

1

Size

243 B

Version

2

Bits

0acb5add

Nonce

2,451,383,702

Timestamp

7/3/2016, 3:21:58 AM

Confirmations

5,180,805

Merkle Root

6400ae360b46b36448c3efa1b64ef713dca0d654f58b977e6631bd91c97fa63e
Transactions (1)
Coinbase6400ae360b46b3…31bd91c97fa63e
1 in β†’ 2 out8.5700 XPM152 B
AGdPoJeN…tYbQQJmTAXbk7f7A…Tx7JECPG
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.

3.007 Γ— 10⁹⁷(98-digit number)
30072110621786247820…92869920384755712000
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
3.007 Γ— 10⁹⁷(98-digit number)
30072110621786247820…92869920384755712001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.014 Γ— 10⁹⁷(98-digit number)
60144221243572495641…85739840769511424001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.202 Γ— 10⁹⁸(99-digit number)
12028844248714499128…71479681539022848001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.405 Γ— 10⁹⁸(99-digit number)
24057688497428998256…42959363078045696001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.811 Γ— 10⁹⁸(99-digit number)
48115376994857996513…85918726156091392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.623 Γ— 10⁹⁸(99-digit number)
96230753989715993026…71837452312182784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.924 Γ— 10⁹⁹(100-digit number)
19246150797943198605…43674904624365568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.849 Γ— 10⁹⁹(100-digit number)
38492301595886397210…87349809248731136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.698 Γ— 10⁹⁹(100-digit number)
76984603191772794421…74699618497462272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.539 Γ— 10¹⁰⁰(101-digit number)
15396920638354558884…49399236994924544001
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 1658292

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 3e3175ddd4ec24002e8bf102c406f0b655763ea6b3e8e3a8f1a466c3a9a35c4f

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 #1,658,292 on Chainz β†—
Circulating Supply:57,957,047 XPMΒ·at block #6,839,096 Β· updates every 60s
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