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Block #2,924,883

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/16/2018, 3:23:12 AM Β· Difficulty 11.3574 Β· 3,916,297 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d5e0b7f762f6ca1d87e991c8bc2db4bf04481a2808bfb0ae55934f97cc7dc8cf
View on Chainz β†—

Difficulty

11.357409

Transactions

1

Size

201 B

Version

2

Bits

0b5b7f20

Nonce

1,867,899,598

Timestamp

11/16/2018, 3:23:12 AM

Confirmations

3,916,297

Merkle Root

6761bffd4e367b7594b90219a7f194df66716c01248d5c7622d64b73372e3696
Transactions (1)
Coinbase6761bffd4e367b…d64b73372e3696
1 in β†’ 1 out7.7400 XPM110 B
AbXwmGxD…4XXYP765
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.

7.812 Γ— 10⁹⁢(97-digit number)
78123615255862888671…41216770057077391360
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
7.812 Γ— 10⁹⁢(97-digit number)
78123615255862888671…41216770057077391361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.562 Γ— 10⁹⁷(98-digit number)
15624723051172577734…82433540114154782721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.124 Γ— 10⁹⁷(98-digit number)
31249446102345155468…64867080228309565441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.249 Γ— 10⁹⁷(98-digit number)
62498892204690310937…29734160456619130881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.249 Γ— 10⁹⁸(99-digit number)
12499778440938062187…59468320913238261761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.499 Γ— 10⁹⁸(99-digit number)
24999556881876124374…18936641826476523521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.999 Γ— 10⁹⁸(99-digit number)
49999113763752248749…37873283652953047041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.999 Γ— 10⁹⁸(99-digit number)
99998227527504497499…75746567305906094081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.999 Γ— 10⁹⁹(100-digit number)
19999645505500899499…51493134611812188161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.999 Γ— 10⁹⁹(100-digit number)
39999291011001798999…02986269223624376321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.999 Γ— 10⁹⁹(100-digit number)
79998582022003597999…05972538447248752641
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 2924883

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 d5e0b7f762f6ca1d87e991c8bc2db4bf04481a2808bfb0ae55934f97cc7dc8cf

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 #2,924,883 on Chainz β†—
Circulating Supply:57,973,799 XPMΒ·at block #6,841,179 Β· updates every 60s
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