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Home/Chain Registry/Block #1,580,991

Block #1,580,991

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/12/2016, 2:56:24 AM Β· Difficulty 10.6656 Β· 5,261,053 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f4067a7dbd40d349c2d36c9c0ea6316b5652ef7484c53283797c907891367068
View on Chainz β†—

Difficulty

10.665639

Transactions

1

Size

242 B

Version

2

Bits

0aaa674f

Nonce

634,249,086

Timestamp

5/12/2016, 2:56:24 AM

Confirmations

5,261,053

Merkle Root

8512670083d56b814ac1862c555810bac5e473415a1ddfb81b698d49274a5345
Transactions (1)
Coinbase8512670083d56b…698d49274a5345
1 in β†’ 2 out8.7800 XPM152 B
AXZf8xqq…hQwCQgXtALPu3s2c…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.

4.097 Γ— 10⁹⁡(96-digit number)
40979089113963811269…52509695368367216320
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
4.097 Γ— 10⁹⁡(96-digit number)
40979089113963811269…52509695368367216319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.195 Γ— 10⁹⁡(96-digit number)
81958178227927622538…05019390736734432639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.639 Γ— 10⁹⁢(97-digit number)
16391635645585524507…10038781473468865279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.278 Γ— 10⁹⁢(97-digit number)
32783271291171049015…20077562946937730559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.556 Γ— 10⁹⁢(97-digit number)
65566542582342098030…40155125893875461119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.311 Γ— 10⁹⁷(98-digit number)
13113308516468419606…80310251787750922239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.622 Γ— 10⁹⁷(98-digit number)
26226617032936839212…60620503575501844479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.245 Γ— 10⁹⁷(98-digit number)
52453234065873678424…21241007151003688959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.049 Γ— 10⁹⁸(99-digit number)
10490646813174735684…42482014302007377919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.098 Γ— 10⁹⁸(99-digit number)
20981293626349471369…84964028604014755839
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 1580991

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 f4067a7dbd40d349c2d36c9c0ea6316b5652ef7484c53283797c907891367068

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 #1,580,991 on Chainz β†—
Circulating Supply:57,980,742 XPMΒ·at block #6,842,043 Β· updates every 60s
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