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Block #1,681,644

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2016, 11:43:23 AM Β· Difficulty 10.7165 Β· 5,155,001 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
157d414a1e56b34cf158ee56ccae92e85f3f22660d5fa59552bd5cbaf7956fa4
View on Chainz β†—

Difficulty

10.716500

Transactions

1

Size

242 B

Version

2

Bits

0ab76c92

Nonce

1,377,678,034

Timestamp

7/20/2016, 11:43:23 AM

Confirmations

5,155,001

Merkle Root

933a3815bb4a1658e1dbbd48da62f2ad4698f9f5dda61d1cb97e0cb0b24bd0ba
Transactions (1)
Coinbase933a3815bb4a16…7e0cb0b24bd0ba
1 in β†’ 2 out8.6900 XPM152 B
AW7XpJLz…npEJgCfvALPu3s2c…EJXLjVFh
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.

5.150 Γ— 10⁹⁴(95-digit number)
51508264614691476940…34683930829436195010
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
5.150 Γ— 10⁹⁴(95-digit number)
51508264614691476940…34683930829436195009
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.030 Γ— 10⁹⁡(96-digit number)
10301652922938295388…69367861658872390019
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.060 Γ— 10⁹⁡(96-digit number)
20603305845876590776…38735723317744780039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.120 Γ— 10⁹⁡(96-digit number)
41206611691753181552…77471446635489560079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.241 Γ— 10⁹⁡(96-digit number)
82413223383506363104…54942893270979120159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.648 Γ— 10⁹⁢(97-digit number)
16482644676701272620…09885786541958240319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.296 Γ— 10⁹⁢(97-digit number)
32965289353402545241…19771573083916480639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.593 Γ— 10⁹⁢(97-digit number)
65930578706805090483…39543146167832961279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.318 Γ— 10⁹⁷(98-digit number)
13186115741361018096…79086292335665922559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.637 Γ— 10⁹⁷(98-digit number)
26372231482722036193…58172584671331845119
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 1681644

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 157d414a1e56b34cf158ee56ccae92e85f3f22660d5fa59552bd5cbaf7956fa4

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 #1,681,644 on Chainz β†—
Circulating Supply:57,937,435 XPMΒ·at block #6,836,644 Β· updates every 60s
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