XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,066,153

Block #1,066,153

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/19/2015, 9:16:45 AM Β· Difficulty 10.7363 Β· 5,739,123 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
255e557407b99c80c24dbb846c2df7a93fea0ed2cd54348fc743f14f36db6d65
View on Chainz β†—

Difficulty

10.736337

Transactions

1

Size

207 B

Version

2

Bits

0abc8092

Nonce

636,136,037

Timestamp

5/19/2015, 9:16:45 AM

Confirmations

5,739,123

Merkle Root

a4aec3d20252bf490c58aea719c71f78d9ec09dc7bc8fa7f552db479de1175b3
Transactions (1)
Coinbasea4aec3d20252bf…2db479de1175b3
1 in β†’ 1 out8.6600 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.236 Γ— 10⁹⁷(98-digit number)
22368119514206943229…55440255031468889600
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
2.236 Γ— 10⁹⁷(98-digit number)
22368119514206943229…55440255031468889601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.473 Γ— 10⁹⁷(98-digit number)
44736239028413886459…10880510062937779201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.947 Γ— 10⁹⁷(98-digit number)
89472478056827772918…21761020125875558401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.789 Γ— 10⁹⁸(99-digit number)
17894495611365554583…43522040251751116801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.578 Γ— 10⁹⁸(99-digit number)
35788991222731109167…87044080503502233601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.157 Γ— 10⁹⁸(99-digit number)
71577982445462218334…74088161007004467201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.431 Γ— 10⁹⁹(100-digit number)
14315596489092443666…48176322014008934401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.863 Γ— 10⁹⁹(100-digit number)
28631192978184887333…96352644028017868801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.726 Γ— 10⁹⁹(100-digit number)
57262385956369774667…92705288056035737601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.145 Γ— 10¹⁰⁰(101-digit number)
11452477191273954933…85410576112071475201
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 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
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 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 1066153

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 255e557407b99c80c24dbb846c2df7a93fea0ed2cd54348fc743f14f36db6d65

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 #1,066,153 on Chainz β†—
Circulating Supply:57,686,280 XPMΒ·at block #6,805,275 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.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK