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Block #2,676,642

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/25/2018, 12:31:26 AM Β· Difficulty 11.6979 Β· 4,163,987 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a731003cec1162e928bdc8ab3daf87eb0d694766a3a3d1fe30e64a7945d1f953
View on Chainz β†—

Difficulty

11.697903

Transactions

1

Size

200 B

Version

2

Bits

0bb2a9c8

Nonce

608,278,710

Timestamp

5/25/2018, 12:31:26 AM

Confirmations

4,163,987

Merkle Root

a3ad853967c01213c15060ade2c79e15df1265d4634b6585e996cd21fb54bb44
Transactions (1)
Coinbasea3ad853967c012…96cd21fb54bb44
1 in β†’ 1 out7.3000 XPM109 B
ALENKess…6TRhhxb8
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.

2.081 Γ— 10⁹⁷(98-digit number)
20814551511396791385…21214377573795809280
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.081 Γ— 10⁹⁷(98-digit number)
20814551511396791385…21214377573795809279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.162 Γ— 10⁹⁷(98-digit number)
41629103022793582770…42428755147591618559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.325 Γ— 10⁹⁷(98-digit number)
83258206045587165541…84857510295183237119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.665 Γ— 10⁹⁸(99-digit number)
16651641209117433108…69715020590366474239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.330 Γ— 10⁹⁸(99-digit number)
33303282418234866216…39430041180732948479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.660 Γ— 10⁹⁸(99-digit number)
66606564836469732433…78860082361465896959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.332 Γ— 10⁹⁹(100-digit number)
13321312967293946486…57720164722931793919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.664 Γ— 10⁹⁹(100-digit number)
26642625934587892973…15440329445863587839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.328 Γ— 10⁹⁹(100-digit number)
53285251869175785946…30880658891727175679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.065 Γ— 10¹⁰⁰(101-digit number)
10657050373835157189…61761317783454351359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.131 Γ— 10¹⁰⁰(101-digit number)
21314100747670314378…23522635566908702719
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2676642

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 a731003cec1162e928bdc8ab3daf87eb0d694766a3a3d1fe30e64a7945d1f953

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 #2,676,642 on Chainz β†—
Circulating Supply:57,969,372 XPMΒ·at block #6,840,628 Β· updates every 60s
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