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Home/Chain Registry/Block #1,448,721

Block #1,448,721

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/9/2016, 2:03:22 AM Β· Difficulty 10.7574 Β· 5,393,524 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bfc62de053f7258e366ef8a935cb702a19160ab0154262aa60712defa7452ff5
View on Chainz β†—

Difficulty

10.757436

Transactions

1

Size

199 B

Version

2

Bits

0ac1e758

Nonce

903,757,034

Timestamp

2/9/2016, 2:03:22 AM

Confirmations

5,393,524

Merkle Root

60b13aa288bd82ae7ea2cad309926f80f4802323d7e096da1afbd1c3059fa460
Transactions (1)
Coinbase60b13aa288bd82…fbd1c3059fa460
1 in β†’ 1 out8.6300 XPM109 B
AQHmba9V…58UeyaAJ
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.

6.160 Γ— 10⁹³(94-digit number)
61601601678864665432…20181011104119936960
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
6.160 Γ— 10⁹³(94-digit number)
61601601678864665432…20181011104119936961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.232 Γ— 10⁹⁴(95-digit number)
12320320335772933086…40362022208239873921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.464 Γ— 10⁹⁴(95-digit number)
24640640671545866172…80724044416479747841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.928 Γ— 10⁹⁴(95-digit number)
49281281343091732345…61448088832959495681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.856 Γ— 10⁹⁴(95-digit number)
98562562686183464691…22896177665918991361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.971 Γ— 10⁹⁡(96-digit number)
19712512537236692938…45792355331837982721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.942 Γ— 10⁹⁡(96-digit number)
39425025074473385876…91584710663675965441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.885 Γ— 10⁹⁡(96-digit number)
78850050148946771752…83169421327351930881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.577 Γ— 10⁹⁢(97-digit number)
15770010029789354350…66338842654703861761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.154 Γ— 10⁹⁢(97-digit number)
31540020059578708701…32677685309407723521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.308 Γ— 10⁹⁢(97-digit number)
63080040119157417402…65355370618815447041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second 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
RareChain length 11
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 1448721

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 bfc62de053f7258e366ef8a935cb702a19160ab0154262aa60712defa7452ff5

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 #1,448,721 on Chainz β†—
Circulating Supply:57,982,358 XPMΒ·at block #6,842,244 Β· updates every 60s
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