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Block #2,648,577

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/4/2018, 2:58:33 PM Β· Difficulty 11.7663 Β· 4,196,808 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a0c2de8fc11dd77d8c9efacde69398de225aae6071cb465c1fce52dde8170adf
View on Chainz β†—

Difficulty

11.766266

Transactions

1

Size

200 B

Version

2

Bits

0bc429fc

Nonce

464,433,860

Timestamp

5/4/2018, 2:58:33 PM

Confirmations

4,196,808

Merkle Root

95a8b2d5a4eb0e13e81cdcaf5f9c8f01cd1928a1f0fcfaab13875b7bf81584ff
Transactions (1)
Coinbase95a8b2d5a4eb0e…875b7bf81584ff
1 in β†’ 1 out7.2100 XPM110 B
AWtvGFTh…fXRDqSNE
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.

1.118 Γ— 10⁹⁡(96-digit number)
11180585737725887113…67267474989040176640
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
1.118 Γ— 10⁹⁡(96-digit number)
11180585737725887113…67267474989040176641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.236 Γ— 10⁹⁡(96-digit number)
22361171475451774226…34534949978080353281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.472 Γ— 10⁹⁡(96-digit number)
44722342950903548452…69069899956160706561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.944 Γ— 10⁹⁡(96-digit number)
89444685901807096905…38139799912321413121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.788 Γ— 10⁹⁢(97-digit number)
17888937180361419381…76279599824642826241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.577 Γ— 10⁹⁢(97-digit number)
35777874360722838762…52559199649285652481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.155 Γ— 10⁹⁢(97-digit number)
71555748721445677524…05118399298571304961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.431 Γ— 10⁹⁷(98-digit number)
14311149744289135504…10236798597142609921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.862 Γ— 10⁹⁷(98-digit number)
28622299488578271009…20473597194285219841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.724 Γ— 10⁹⁷(98-digit number)
57244598977156542019…40947194388570439681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.144 Γ— 10⁹⁸(99-digit number)
11448919795431308403…81894388777140879361
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 2648577

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 a0c2de8fc11dd77d8c9efacde69398de225aae6071cb465c1fce52dde8170adf

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 #2,648,577 on Chainz β†—
Circulating Supply:58,007,524 XPMΒ·at block #6,845,384 Β· updates every 60s
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