XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,135,743

Block #2,135,743

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 5/28/2017, 12:37:44 PM Β· Difficulty 10.8987 Β· 4,706,803 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a8d4734c64361954e2dd2a6a997032983118a306e3ff6d66e7035341ce0f7028
View on Chainz β†—

Difficulty

10.898729

Transactions

1

Size

200 B

Version

2

Bits

0ae6131d

Nonce

404,219,085

Timestamp

5/28/2017, 12:37:44 PM

Confirmations

4,706,803

Merkle Root

01b704226c14a5bea12711597b6978994309c201a05df0b899b848dd62215b28
Transactions (1)
Coinbase01b704226c14a5…b848dd62215b28
1 in β†’ 1 out8.4100 XPM109 B
AeBqhzVr…cKwuGQ3U
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.

7.450 Γ— 10⁹⁡(96-digit number)
74505860696754189396…33181328896018216960
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
7.450 Γ— 10⁹⁡(96-digit number)
74505860696754189396…33181328896018216959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.490 Γ— 10⁹⁢(97-digit number)
14901172139350837879…66362657792036433919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.980 Γ— 10⁹⁢(97-digit number)
29802344278701675758…32725315584072867839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.960 Γ— 10⁹⁢(97-digit number)
59604688557403351516…65450631168145735679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.192 Γ— 10⁹⁷(98-digit number)
11920937711480670303…30901262336291471359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.384 Γ— 10⁹⁷(98-digit number)
23841875422961340606…61802524672582942719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.768 Γ— 10⁹⁷(98-digit number)
47683750845922681213…23605049345165885439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.536 Γ— 10⁹⁷(98-digit number)
95367501691845362427…47210098690331770879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.907 Γ— 10⁹⁸(99-digit number)
19073500338369072485…94420197380663541759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.814 Γ— 10⁹⁸(99-digit number)
38147000676738144970…88840394761327083519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.629 Γ— 10⁹⁸(99-digit number)
76294001353476289941…77680789522654167039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.525 Γ— 10⁹⁹(100-digit number)
15258800270695257988…55361579045308334079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2135743

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 a8d4734c64361954e2dd2a6a997032983118a306e3ff6d66e7035341ce0f7028

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 #2,135,743 on Chainz β†—
Circulating Supply:57,984,792 XPMΒ·at block #6,842,545 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy