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Home/Chain Registry/Block #1,294,321

Block #1,294,321

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/22/2015, 7:03:51 PM Β· Difficulty 10.8615 Β· 5,502,032 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
66e49d26e46e842c5d5f65e03b80847657b7950dfef8383814cbe86da9c1e360
View on Chainz β†—

Difficulty

10.861465

Transactions

1

Size

199 B

Version

2

Bits

0adc88f1

Nonce

965,387,499

Timestamp

10/22/2015, 7:03:51 PM

Confirmations

5,502,032

Merkle Root

a3aaecef851bb42f2c4f857fa5a78834f7d88f68ffdb113642e1d7514521188f
Transactions (1)
Coinbasea3aaecef851bb4…e1d7514521188f
1 in β†’ 1 out8.4600 XPM109 B
AcXooEoA…eTCufinQ
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.

1.644 Γ— 10⁹⁴(95-digit number)
16444387296341756065…96403533688445030400
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
1.644 Γ— 10⁹⁴(95-digit number)
16444387296341756065…96403533688445030399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.288 Γ— 10⁹⁴(95-digit number)
32888774592683512130…92807067376890060799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.577 Γ— 10⁹⁴(95-digit number)
65777549185367024260…85614134753780121599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.315 Γ— 10⁹⁡(96-digit number)
13155509837073404852…71228269507560243199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.631 Γ— 10⁹⁡(96-digit number)
26311019674146809704…42456539015120486399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.262 Γ— 10⁹⁡(96-digit number)
52622039348293619408…84913078030240972799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.052 Γ— 10⁹⁢(97-digit number)
10524407869658723881…69826156060481945599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.104 Γ— 10⁹⁢(97-digit number)
21048815739317447763…39652312120963891199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.209 Γ— 10⁹⁢(97-digit number)
42097631478634895526…79304624241927782399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.419 Γ— 10⁹⁢(97-digit number)
84195262957269791053…58609248483855564799
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 1294321

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 66e49d26e46e842c5d5f65e03b80847657b7950dfef8383814cbe86da9c1e360

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 #1,294,321 on Chainz β†—
Circulating Supply:57,614,818 XPMΒ·at block #6,796,352 Β· updates every 60s
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