XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #3,002,675

Block #3,002,675

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/9/2019, 10:33:12 PM Β· Difficulty 11.2017 Β· 3,835,965 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bf12eaa11e7e01f1153c857a272adb4ddd8d20322c748a13a507a5bcf9f4d3cc
View on Chainz β†—

Difficulty

11.201742

Transactions

3

Size

814 B

Version

2

Bits

0b33a55c

Nonce

401,812,505

Timestamp

1/9/2019, 10:33:12 PM

Confirmations

3,835,965

Merkle Root

4ba9a4388b8d167e5d723f27fd84368b1b6d7765e565035db6ad149d5cd0d019
Transactions (3)
Coinbase7194403037f655…115815c46b9ced
1 in β†’ 1 out7.9800 XPM110 B
AbXwmGxD…4XXYP765
f97616dedfd3e2…4c882bc99399b6
3 in β†’ 2 out23.7500 XPM420 B
AemY4Zt4…87UF1iHfAUhjokok…k5m93PZR
968552b64fd504…93c004391ff589
1 in β†’ 2 out7.9100 XPM193 B
AeSNwRM1…5oshdL2YAUhjokok…k5m93PZR
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.

8.935 Γ— 10⁹⁢(97-digit number)
89359533840183239140…10512765861585715200
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
8.935 Γ— 10⁹⁢(97-digit number)
89359533840183239140…10512765861585715201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.787 Γ— 10⁹⁷(98-digit number)
17871906768036647828…21025531723171430401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.574 Γ— 10⁹⁷(98-digit number)
35743813536073295656…42051063446342860801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.148 Γ— 10⁹⁷(98-digit number)
71487627072146591312…84102126892685721601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.429 Γ— 10⁹⁸(99-digit number)
14297525414429318262…68204253785371443201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.859 Γ— 10⁹⁸(99-digit number)
28595050828858636525…36408507570742886401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.719 Γ— 10⁹⁸(99-digit number)
57190101657717273050…72817015141485772801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.143 Γ— 10⁹⁹(100-digit number)
11438020331543454610…45634030282971545601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.287 Γ— 10⁹⁹(100-digit number)
22876040663086909220…91268060565943091201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.575 Γ— 10⁹⁹(100-digit number)
45752081326173818440…82536121131886182401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.150 Γ— 10⁹⁹(100-digit number)
91504162652347636880…65072242263772364801
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 3002675

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 bf12eaa11e7e01f1153c857a272adb4ddd8d20322c748a13a507a5bcf9f4d3cc

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 #3,002,675 on Chainz β†—
Circulating Supply:57,953,384 XPMΒ·at block #6,838,639 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy