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Home/Chain Registry/Block #2,875,989

Block #2,875,989

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/10/2018, 11:13:11 PM Β· Difficulty 11.6577 Β· 3,967,255 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a7baaa1da5ac31a6f048f3d9d4556f81fa927dfa6fc45535cc0abdf3d5299f72
View on Chainz β†—

Difficulty

11.657683

Transactions

1

Size

200 B

Version

2

Bits

0ba85de5

Nonce

984,633,524

Timestamp

10/10/2018, 11:13:11 PM

Confirmations

3,967,255

Merkle Root

16d3ceec7a82b3c88836b2e3c3074d2d0900cb74953d8d24b9e32479888fda26
Transactions (1)
Coinbase16d3ceec7a82b3…e32479888fda26
1 in β†’ 1 out7.3500 XPM109 B
ATqikCqK…72MHycMW
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.

1.013 Γ— 10⁹⁷(98-digit number)
10135803450687368672…22405335992423190400
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
1.013 Γ— 10⁹⁷(98-digit number)
10135803450687368672…22405335992423190401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.027 Γ— 10⁹⁷(98-digit number)
20271606901374737345…44810671984846380801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.054 Γ— 10⁹⁷(98-digit number)
40543213802749474690…89621343969692761601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.108 Γ— 10⁹⁷(98-digit number)
81086427605498949381…79242687939385523201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.621 Γ— 10⁹⁸(99-digit number)
16217285521099789876…58485375878771046401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.243 Γ— 10⁹⁸(99-digit number)
32434571042199579752…16970751757542092801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.486 Γ— 10⁹⁸(99-digit number)
64869142084399159505…33941503515084185601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.297 Γ— 10⁹⁹(100-digit number)
12973828416879831901…67883007030168371201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.594 Γ— 10⁹⁹(100-digit number)
25947656833759663802…35766014060336742401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.189 Γ— 10⁹⁹(100-digit number)
51895313667519327604…71532028120673484801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.037 Γ— 10¹⁰⁰(101-digit number)
10379062733503865520…43064056241346969601
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 2875989

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 a7baaa1da5ac31a6f048f3d9d4556f81fa927dfa6fc45535cc0abdf3d5299f72

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 #2,875,989 on Chainz β†—
Circulating Supply:57,990,327 XPMΒ·at block #6,843,243 Β· updates every 60s
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