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Home/Chain Registry/Block #2,671,457

Block #2,671,457

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/21/2018, 12:31:04 PM Β· Difficulty 11.6889 Β· 4,169,992 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a5b481bd023b04a7fb346e6cd5d991093588a4717ea287b2b42046c5fe7e7796
View on Chainz β†—

Difficulty

11.688880

Transactions

1

Size

200 B

Version

2

Bits

0bb05a6a

Nonce

1,657,912,133

Timestamp

5/21/2018, 12:31:04 PM

Confirmations

4,169,992

Merkle Root

1ac32b6b54f91ab1ae1e436864d67cf739a566ceaa3948ae95de90cc795b1e36
Transactions (1)
Coinbase1ac32b6b54f91a…de90cc795b1e36
1 in β†’ 1 out7.3100 XPM109 B
ARvNmTN8…CcKt3mUD
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.

9.402 Γ— 10⁹⁢(97-digit number)
94027050876016739653…87762669670948700160
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
9.402 Γ— 10⁹⁢(97-digit number)
94027050876016739653…87762669670948700159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.880 Γ— 10⁹⁷(98-digit number)
18805410175203347930…75525339341897400319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.761 Γ— 10⁹⁷(98-digit number)
37610820350406695861…51050678683794800639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.522 Γ— 10⁹⁷(98-digit number)
75221640700813391722…02101357367589601279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.504 Γ— 10⁹⁸(99-digit number)
15044328140162678344…04202714735179202559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.008 Γ— 10⁹⁸(99-digit number)
30088656280325356689…08405429470358405119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.017 Γ— 10⁹⁸(99-digit number)
60177312560650713378…16810858940716810239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.203 Γ— 10⁹⁹(100-digit number)
12035462512130142675…33621717881433620479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.407 Γ— 10⁹⁹(100-digit number)
24070925024260285351…67243435762867240959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.814 Γ— 10⁹⁹(100-digit number)
48141850048520570702…34486871525734481919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.628 Γ— 10⁹⁹(100-digit number)
96283700097041141405…68973743051468963839
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 2671457

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 a5b481bd023b04a7fb346e6cd5d991093588a4717ea287b2b42046c5fe7e7796

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 #2,671,457 on Chainz β†—
Circulating Supply:57,975,971 XPMΒ·at block #6,841,448 Β· updates every 60s
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