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Block #1,524,393

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2016, 10:05:06 AM Β· Difficulty 10.5998 Β· 5,301,895 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
687e2414599a5c41fe8b1aee76e578b86587372aa21feb07f17b581d1bc9c8d3
View on Chainz β†—

Difficulty

10.599837

Transactions

1

Size

199 B

Version

2

Bits

0a998ee7

Nonce

988,174,471

Timestamp

4/3/2016, 10:05:06 AM

Confirmations

5,301,895

Merkle Root

6d9c9c3aac0fe184c8d20523f46e4dcdb77a8d45b71982220f7afbf91d9ade63
Transactions (1)
Coinbase6d9c9c3aac0fe1…7afbf91d9ade63
1 in β†’ 1 out8.8900 XPM109 B
AMnS9zky…kC77s7J8
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.

2.572 Γ— 10⁹⁴(95-digit number)
25723144608445731629…44846275964441006240
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
2.572 Γ— 10⁹⁴(95-digit number)
25723144608445731629…44846275964441006239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.144 Γ— 10⁹⁴(95-digit number)
51446289216891463259…89692551928882012479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.028 Γ— 10⁹⁡(96-digit number)
10289257843378292651…79385103857764024959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.057 Γ— 10⁹⁡(96-digit number)
20578515686756585303…58770207715528049919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.115 Γ— 10⁹⁡(96-digit number)
41157031373513170607…17540415431056099839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.231 Γ— 10⁹⁡(96-digit number)
82314062747026341214…35080830862112199679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.646 Γ— 10⁹⁢(97-digit number)
16462812549405268242…70161661724224399359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.292 Γ— 10⁹⁢(97-digit number)
32925625098810536485…40323323448448798719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.585 Γ— 10⁹⁢(97-digit number)
65851250197621072971…80646646896897597439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.317 Γ— 10⁹⁷(98-digit number)
13170250039524214594…61293293793795194879
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 1524393

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 687e2414599a5c41fe8b1aee76e578b86587372aa21feb07f17b581d1bc9c8d3

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 #1,524,393 on Chainz β†—
Circulating Supply:57,854,443 XPMΒ·at block #6,826,287 Β· updates every 60s
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