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Home/Chain Registry/Block #1,697,038

Block #1,697,038

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/31/2016, 3:57:55 PM Β· Difficulty 10.6749 Β· 5,145,730 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cd8d9727db608bbfc69a2b58d4449d9a0e9261c7e1c8ad703edf36ce0e8da3e1
View on Chainz β†—

Difficulty

10.674925

Transactions

2

Size

1.54 KB

Version

2

Bits

0aacc7ea

Nonce

766,745,233

Timestamp

7/31/2016, 3:57:55 PM

Confirmations

5,145,730

Merkle Root

c4952bad4ee83cd7628e61939159f5c6f176d75e1a49a3b841d7a99e97c5ec1c
Transactions (2)
Coinbase4caf95fbd97611…c5f24c57fd7d9c
1 in β†’ 1 out8.7806 XPM110 B
AJi2W6Cs…n8sGWvkg
b6a030659e5f28…b05b9c12928fba
9 in β†’ 1 out0.8910 XPM1.34 KB
AdiTsMuZ…kFyzR8oM
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.

2.863 Γ— 10⁹⁡(96-digit number)
28633720947066472680…39252312866832155360
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.863 Γ— 10⁹⁡(96-digit number)
28633720947066472680…39252312866832155359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.726 Γ— 10⁹⁡(96-digit number)
57267441894132945361…78504625733664310719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.145 Γ— 10⁹⁢(97-digit number)
11453488378826589072…57009251467328621439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.290 Γ— 10⁹⁢(97-digit number)
22906976757653178144…14018502934657242879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.581 Γ— 10⁹⁢(97-digit number)
45813953515306356289…28037005869314485759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.162 Γ— 10⁹⁢(97-digit number)
91627907030612712578…56074011738628971519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.832 Γ— 10⁹⁷(98-digit number)
18325581406122542515…12148023477257943039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.665 Γ— 10⁹⁷(98-digit number)
36651162812245085031…24296046954515886079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.330 Γ— 10⁹⁷(98-digit number)
73302325624490170063…48592093909031772159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.466 Γ— 10⁹⁸(99-digit number)
14660465124898034012…97184187818063544319
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 1697038

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 cd8d9727db608bbfc69a2b58d4449d9a0e9261c7e1c8ad703edf36ce0e8da3e1

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 #1,697,038 on Chainz β†—
Circulating Supply:57,986,483 XPMΒ·at block #6,842,767 Β· updates every 60s
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