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Home/Chain Registry/Block #2,646,708

Block #2,646,708

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 12:14:48 PM Β· Difficulty 11.7535 Β· 4,192,670 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c3010ed2f17dcbdacd5103a521cd179caf47602b53eba1d6e99044942b37222d
View on Chainz β†—

Difficulty

11.753474

Transactions

1

Size

200 B

Version

2

Bits

0bc0e3b0

Nonce

430,369,436

Timestamp

5/3/2018, 12:14:48 PM

Confirmations

4,192,670

Merkle Root

acde16b25365be23d877cbf0f6c99210b7199ff957cd11fb9d38dae9db5ac09b
Transactions (1)
Coinbaseacde16b25365be…38dae9db5ac09b
1 in β†’ 1 out7.2300 XPM110 B
Adqah8zh…1WwoHJ9t
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.

2.969 Γ— 10⁹⁴(95-digit number)
29698383688280296553…78727426589062676480
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
2.969 Γ— 10⁹⁴(95-digit number)
29698383688280296553…78727426589062676481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.939 Γ— 10⁹⁴(95-digit number)
59396767376560593107…57454853178125352961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.187 Γ— 10⁹⁡(96-digit number)
11879353475312118621…14909706356250705921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.375 Γ— 10⁹⁡(96-digit number)
23758706950624237243…29819412712501411841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.751 Γ— 10⁹⁡(96-digit number)
47517413901248474486…59638825425002823681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.503 Γ— 10⁹⁡(96-digit number)
95034827802496948972…19277650850005647361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.900 Γ— 10⁹⁢(97-digit number)
19006965560499389794…38555301700011294721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.801 Γ— 10⁹⁢(97-digit number)
38013931120998779588…77110603400022589441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.602 Γ— 10⁹⁢(97-digit number)
76027862241997559177…54221206800045178881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.520 Γ— 10⁹⁷(98-digit number)
15205572448399511835…08442413600090357761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.041 Γ— 10⁹⁷(98-digit number)
30411144896799023671…16884827200180715521
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 2646708

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 c3010ed2f17dcbdacd5103a521cd179caf47602b53eba1d6e99044942b37222d

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 #2,646,708 on Chainz β†—
Circulating Supply:57,959,307 XPMΒ·at block #6,839,377 Β· updates every 60s
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