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Home/Chain Registry/Block #2,642,658

Block #2,642,658

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/1/2018, 7:44:05 PM Β· Difficulty 11.6599 Β· 4,193,707 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9fe60c5d9df9f83b0e081b36982271c58d40c7ee1218f45ccbfd6776d2e8ed45
View on Chainz β†—

Difficulty

11.659874

Transactions

1

Size

200 B

Version

2

Bits

0ba8ed85

Nonce

145,171,250

Timestamp

5/1/2018, 7:44:05 PM

Confirmations

4,193,707

Merkle Root

5785d392b5b60d6d3dd7a330cd6582343bf156bb97d237848ce3937a7da1be0f
Transactions (1)
Coinbase5785d392b5b60d…e3937a7da1be0f
1 in β†’ 1 out7.3400 XPM110 B
APzgNEqQ…N4RbqbeV
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.

3.117 Γ— 10⁹⁴(95-digit number)
31177012168532575765…09348477042836577220
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
3.117 Γ— 10⁹⁴(95-digit number)
31177012168532575765…09348477042836577221
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.235 Γ— 10⁹⁴(95-digit number)
62354024337065151530…18696954085673154441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.247 Γ— 10⁹⁡(96-digit number)
12470804867413030306…37393908171346308881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.494 Γ— 10⁹⁡(96-digit number)
24941609734826060612…74787816342692617761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.988 Γ— 10⁹⁡(96-digit number)
49883219469652121224…49575632685385235521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.976 Γ— 10⁹⁡(96-digit number)
99766438939304242449…99151265370770471041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.995 Γ— 10⁹⁢(97-digit number)
19953287787860848489…98302530741540942081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.990 Γ— 10⁹⁢(97-digit number)
39906575575721696979…96605061483081884161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.981 Γ— 10⁹⁢(97-digit number)
79813151151443393959…93210122966163768321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.596 Γ— 10⁹⁷(98-digit number)
15962630230288678791…86420245932327536641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.192 Γ— 10⁹⁷(98-digit number)
31925260460577357583…72840491864655073281
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 2642658

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 9fe60c5d9df9f83b0e081b36982271c58d40c7ee1218f45ccbfd6776d2e8ed45

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 #2,642,658 on Chainz β†—
Circulating Supply:57,935,179 XPMΒ·at block #6,836,364 Β· updates every 60s
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