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Home/Chain Registry/Block #2,646,996

Block #2,646,996

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 5/3/2018, 3:57:33 PM Β· Difficulty 11.7566 Β· 4,186,410 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
16b4abacc10bd31ffd0b8bfae1270e0fe12fc52707dca9009ec3019ee2be1eac
View on Chainz β†—

Difficulty

11.756646

Transactions

1

Size

200 B

Version

2

Bits

0bc1b38b

Nonce

293,553,091

Timestamp

5/3/2018, 3:57:33 PM

Confirmations

4,186,410

Merkle Root

ecb2c28e575409bed391261f6b14e2edba3de6cc4f412574df9f58e07788561d
Transactions (1)
Coinbaseecb2c28e575409…9f58e07788561d
1 in β†’ 1 out7.2200 XPM110 B
AeLPmzob…EZBniiEJ
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.

9.834 Γ— 10⁹⁴(95-digit number)
98349063106076788351…54271398626783406160
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
9.834 Γ— 10⁹⁴(95-digit number)
98349063106076788351…54271398626783406159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.966 Γ— 10⁹⁡(96-digit number)
19669812621215357670…08542797253566812319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.933 Γ— 10⁹⁡(96-digit number)
39339625242430715340…17085594507133624639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.867 Γ— 10⁹⁡(96-digit number)
78679250484861430681…34171189014267249279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.573 Γ— 10⁹⁢(97-digit number)
15735850096972286136…68342378028534498559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.147 Γ— 10⁹⁢(97-digit number)
31471700193944572272…36684756057068997119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.294 Γ— 10⁹⁢(97-digit number)
62943400387889144544…73369512114137994239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.258 Γ— 10⁹⁷(98-digit number)
12588680077577828908…46739024228275988479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.517 Γ— 10⁹⁷(98-digit number)
25177360155155657817…93478048456551976959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.035 Γ— 10⁹⁷(98-digit number)
50354720310311315635…86956096913103953919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.007 Γ— 10⁹⁸(99-digit number)
10070944062062263127…73912193826207907839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
2.014 Γ— 10⁹⁸(99-digit number)
20141888124124526254…47824387652415815679
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 2646996

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 16b4abacc10bd31ffd0b8bfae1270e0fe12fc52707dca9009ec3019ee2be1eac

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 #2,646,996 on Chainz β†—
Circulating Supply:57,911,449 XPMΒ·at block #6,833,405 Β· updates every 60s
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