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Block #1,693,745

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/29/2016, 8:05:27 AM Β· Difficulty 10.6786 Β· 5,123,872 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f06216c0e30ae0b143783c8abecd2daf9b02f4709abf4e7452873478daad031f
View on Chainz β†—

Difficulty

10.678586

Transactions

1

Size

199 B

Version

2

Bits

0aadb7ce

Nonce

197,775,249

Timestamp

7/29/2016, 8:05:27 AM

Confirmations

5,123,872

Merkle Root

9a1e63431a7ae675f0a302b646720bc04f5cd53cc70203c809bd8950aabfcd30
Transactions (1)
Coinbase9a1e63431a7ae6…bd8950aabfcd30
1 in β†’ 1 out8.7600 XPM109 B
AM8BAtZv…YL17U7D2
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.

1.681 Γ— 10⁹⁡(96-digit number)
16815946659374973326…22564221455254617600
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
1.681 Γ— 10⁹⁡(96-digit number)
16815946659374973326…22564221455254617601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.363 Γ— 10⁹⁡(96-digit number)
33631893318749946653…45128442910509235201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.726 Γ— 10⁹⁡(96-digit number)
67263786637499893307…90256885821018470401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.345 Γ— 10⁹⁢(97-digit number)
13452757327499978661…80513771642036940801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.690 Γ— 10⁹⁢(97-digit number)
26905514654999957322…61027543284073881601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.381 Γ— 10⁹⁢(97-digit number)
53811029309999914645…22055086568147763201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.076 Γ— 10⁹⁷(98-digit number)
10762205861999982929…44110173136295526401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.152 Γ— 10⁹⁷(98-digit number)
21524411723999965858…88220346272591052801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.304 Γ— 10⁹⁷(98-digit number)
43048823447999931716…76440692545182105601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.609 Γ— 10⁹⁷(98-digit number)
86097646895999863433…52881385090364211201
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 1693745

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 f06216c0e30ae0b143783c8abecd2daf9b02f4709abf4e7452873478daad031f

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 #1,693,745 on Chainz β†—
Circulating Supply:57,784,993 XPMΒ·at block #6,817,616 Β· updates every 60s
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