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Block #1,371,825

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/16/2015, 6:44:19 PM Β· Difficulty 10.8103 Β· 5,470,303 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bda88877beb37efb747c57ef2412bde114c88a7ff7da90fc10cdbb3fd47ed7bc
View on Chainz β†—

Difficulty

10.810256

Transactions

1

Size

199 B

Version

2

Bits

0acf6cea

Nonce

370,077,284

Timestamp

12/16/2015, 6:44:19 PM

Confirmations

5,470,303

Merkle Root

8c3e54b4ce2625dc907fd4a82c59cfec41a732c1fdcca948c12dcb788a208765
Transactions (1)
Coinbase8c3e54b4ce2625…2dcb788a208765
1 in β†’ 1 out8.5400 XPM109 B
AGUdDWsM…A5VDxT7t
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.

1.714 Γ— 10⁹⁴(95-digit number)
17146139940594751567…68017104601279434400
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
1.714 Γ— 10⁹⁴(95-digit number)
17146139940594751567…68017104601279434399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.429 Γ— 10⁹⁴(95-digit number)
34292279881189503134…36034209202558868799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.858 Γ— 10⁹⁴(95-digit number)
68584559762379006268…72068418405117737599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.371 Γ— 10⁹⁡(96-digit number)
13716911952475801253…44136836810235475199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.743 Γ— 10⁹⁡(96-digit number)
27433823904951602507…88273673620470950399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.486 Γ— 10⁹⁡(96-digit number)
54867647809903205014…76547347240941900799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.097 Γ— 10⁹⁢(97-digit number)
10973529561980641002…53094694481883801599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.194 Γ— 10⁹⁢(97-digit number)
21947059123961282005…06189388963767603199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.389 Γ— 10⁹⁢(97-digit number)
43894118247922564011…12378777927535206399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.778 Γ— 10⁹⁢(97-digit number)
87788236495845128023…24757555855070412799
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 1371825

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 bda88877beb37efb747c57ef2412bde114c88a7ff7da90fc10cdbb3fd47ed7bc

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 #1,371,825 on Chainz β†—
Circulating Supply:57,981,412 XPMΒ·at block #6,842,127 Β· updates every 60s
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