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Home/Chain Registry/Block #1,723,419

Block #1,723,419

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/18/2016, 8:45:01 PM Β· Difficulty 10.6868 Β· 5,093,172 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ee3486ed68d340f2eb4823a82c50d466d4a5dd17b2dcb736540efb8c74f406bf
View on Chainz β†—

Difficulty

10.686799

Transactions

1

Size

199 B

Version

2

Bits

0aafd217

Nonce

1,246,727,708

Timestamp

8/18/2016, 8:45:01 PM

Confirmations

5,093,172

Merkle Root

20d766951d02b7c99de05a935049f27b41d2863645a4087f9d3ad4286ed7f8a5
Transactions (1)
Coinbase20d766951d02b7…3ad4286ed7f8a5
1 in β†’ 1 out8.7400 XPM109 B
ALeT6mxS…zoJ4jw8X
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.

4.937 Γ— 10⁹⁡(96-digit number)
49378690039403165936…85787466835179179200
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
4.937 Γ— 10⁹⁡(96-digit number)
49378690039403165936…85787466835179179199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.875 Γ— 10⁹⁡(96-digit number)
98757380078806331873…71574933670358358399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.975 Γ— 10⁹⁢(97-digit number)
19751476015761266374…43149867340716716799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.950 Γ— 10⁹⁢(97-digit number)
39502952031522532749…86299734681433433599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.900 Γ— 10⁹⁢(97-digit number)
79005904063045065498…72599469362866867199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.580 Γ— 10⁹⁷(98-digit number)
15801180812609013099…45198938725733734399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.160 Γ— 10⁹⁷(98-digit number)
31602361625218026199…90397877451467468799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.320 Γ— 10⁹⁷(98-digit number)
63204723250436052398…80795754902934937599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.264 Γ— 10⁹⁸(99-digit number)
12640944650087210479…61591509805869875199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.528 Γ— 10⁹⁸(99-digit number)
25281889300174420959…23183019611739750399
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 1723419

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 ee3486ed68d340f2eb4823a82c50d466d4a5dd17b2dcb736540efb8c74f406bf

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 #1,723,419 on Chainz β†—
Circulating Supply:57,776,852 XPMΒ·at block #6,816,590 Β· updates every 60s
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