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Home/Chain Registry/Block #1,105,487

Block #1,105,487

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/15/2015, 12:51:47 AM Β· Difficulty 10.7832 Β· 5,708,347 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
21bde6b8563362f6a1e2ef4f97c08645693ef4be77423fc7feba35da2e3f61c8
View on Chainz β†—

Difficulty

10.783206

Transactions

1

Size

207 B

Version

2

Bits

0ac8802a

Nonce

99,871,922

Timestamp

6/15/2015, 12:51:47 AM

Confirmations

5,708,347

Merkle Root

a7463c0c0c892a7c6a8af6ebc3592ce2adb97bd2bc5e67ddf38cf2684b94e9a2
Transactions (1)
Coinbasea7463c0c0c892a…8cf2684b94e9a2
1 in β†’ 1 out8.5900 XPM116 B
AJCEY9yy…tg97E6zm
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.

5.248 Γ— 10⁹⁢(97-digit number)
52481714481023948751…42849630609034530720
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
5.248 Γ— 10⁹⁢(97-digit number)
52481714481023948751…42849630609034530721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.049 Γ— 10⁹⁷(98-digit number)
10496342896204789750…85699261218069061441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.099 Γ— 10⁹⁷(98-digit number)
20992685792409579500…71398522436138122881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.198 Γ— 10⁹⁷(98-digit number)
41985371584819159001…42797044872276245761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.397 Γ— 10⁹⁷(98-digit number)
83970743169638318002…85594089744552491521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.679 Γ— 10⁹⁸(99-digit number)
16794148633927663600…71188179489104983041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.358 Γ— 10⁹⁸(99-digit number)
33588297267855327200…42376358978209966081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.717 Γ— 10⁹⁸(99-digit number)
67176594535710654401…84752717956419932161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.343 Γ— 10⁹⁹(100-digit number)
13435318907142130880…69505435912839864321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.687 Γ— 10⁹⁹(100-digit number)
26870637814284261760…39010871825679728641
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 1105487

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 21bde6b8563362f6a1e2ef4f97c08645693ef4be77423fc7feba35da2e3f61c8

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 #1,105,487 on Chainz β†—
Circulating Supply:57,754,742 XPMΒ·at block #6,813,833 Β· updates every 60s
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