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Home/Chain Registry/Block #2,259,610

Block #2,259,610

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/20/2017, 3:21:21 AM Β· Difficulty 10.9520 Β· 4,577,238 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ce73e79ea9c31724796e6aa05c9223a2c13f1f7d4443530f593dd408751b5a11
View on Chainz β†—

Difficulty

10.952015

Transactions

1

Size

201 B

Version

2

Bits

0af3b744

Nonce

1,386,777,814

Timestamp

8/20/2017, 3:21:21 AM

Confirmations

4,577,238

Merkle Root

1b6c62139cb80c46368bf5e9043d34433a4574ca31873b7bcf07ccd538566eb8
Transactions (1)
Coinbase1b6c62139cb80c…07ccd538566eb8
1 in β†’ 1 out8.3200 XPM110 B
AR3Ux5Bd…5Hg4QuCe
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.

1.720 Γ— 10⁹⁢(97-digit number)
17203089637187448485…29194241675715709440
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
1.720 Γ— 10⁹⁢(97-digit number)
17203089637187448485…29194241675715709439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.440 Γ— 10⁹⁢(97-digit number)
34406179274374896970…58388483351431418879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.881 Γ— 10⁹⁢(97-digit number)
68812358548749793941…16776966702862837759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.376 Γ— 10⁹⁷(98-digit number)
13762471709749958788…33553933405725675519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.752 Γ— 10⁹⁷(98-digit number)
27524943419499917576…67107866811451351039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.504 Γ— 10⁹⁷(98-digit number)
55049886838999835153…34215733622902702079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.100 Γ— 10⁹⁸(99-digit number)
11009977367799967030…68431467245805404159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.201 Γ— 10⁹⁸(99-digit number)
22019954735599934061…36862934491610808319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.403 Γ— 10⁹⁸(99-digit number)
44039909471199868122…73725868983221616639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.807 Γ— 10⁹⁸(99-digit number)
88079818942399736245…47451737966443233279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2259610

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 ce73e79ea9c31724796e6aa05c9223a2c13f1f7d4443530f593dd408751b5a11

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 #2,259,610 on Chainz β†—
Circulating Supply:57,939,073 XPMΒ·at block #6,836,847 Β· updates every 60s
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