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Block #2,528,601

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/19/2018, 12:26:49 PM Β· Difficulty 10.9847 Β· 4,315,304 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dede77c7f8aba9fe92f0adb92e5df9f981abc420d69ec11b1c7f0efe0186a997
View on Chainz β†—

Difficulty

10.984657

Transactions

1

Size

200 B

Version

2

Bits

0afc127e

Nonce

182,079,855

Timestamp

2/19/2018, 12:26:49 PM

Confirmations

4,315,304

Merkle Root

41aa7b7cf01bfa5fd69a273dd27f5ebc95d18bdebda2eeecb3c1133b271af86a
Transactions (1)
Coinbase41aa7b7cf01bfa…c1133b271af86a
1 in β†’ 1 out8.2700 XPM110 B
AG358J2h…9d5AGTF5
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.

1.646 Γ— 10⁹⁡(96-digit number)
16465319762049217137…72399977770769223680
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
1.646 Γ— 10⁹⁡(96-digit number)
16465319762049217137…72399977770769223679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.293 Γ— 10⁹⁡(96-digit number)
32930639524098434274…44799955541538447359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.586 Γ— 10⁹⁡(96-digit number)
65861279048196868548…89599911083076894719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.317 Γ— 10⁹⁢(97-digit number)
13172255809639373709…79199822166153789439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.634 Γ— 10⁹⁢(97-digit number)
26344511619278747419…58399644332307578879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.268 Γ— 10⁹⁢(97-digit number)
52689023238557494838…16799288664615157759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.053 Γ— 10⁹⁷(98-digit number)
10537804647711498967…33598577329230315519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.107 Γ— 10⁹⁷(98-digit number)
21075609295422997935…67197154658460631039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.215 Γ— 10⁹⁷(98-digit number)
42151218590845995870…34394309316921262079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.430 Γ— 10⁹⁷(98-digit number)
84302437181691991741…68788618633842524159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.686 Γ— 10⁹⁸(99-digit number)
16860487436338398348…37577237267685048319
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 2528601

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 dede77c7f8aba9fe92f0adb92e5df9f981abc420d69ec11b1c7f0efe0186a997

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 #2,528,601 on Chainz β†—
Circulating Supply:57,995,612 XPMΒ·at block #6,843,904 Β· updates every 60s
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