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Home/Chain Registry/Block #2,101,855

Block #2,101,855

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/5/2017, 11:09:25 PM Β· Difficulty 10.8648 Β· 4,735,697 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
532d994dfa50d361802807e0038cdfbb2c2d7ce151a3c924d409722525a33274
View on Chainz β†—

Difficulty

10.864786

Transactions

1

Size

199 B

Version

2

Bits

0add62a4

Nonce

573,737,215

Timestamp

5/5/2017, 11:09:25 PM

Confirmations

4,735,697

Merkle Root

b5f1441dd95dd43292251dc9b4ed6d1b32dda2a23f79917ee9b1cc2580c1bba1
Transactions (1)
Coinbaseb5f1441dd95dd4…b1cc2580c1bba1
1 in β†’ 1 out8.4600 XPM110 B
AQQexU7w…Df2wMUHW
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.

4.618 Γ— 10⁹²(93-digit number)
46183914102174313594…22041998670281493760
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
4.618 Γ— 10⁹²(93-digit number)
46183914102174313594…22041998670281493761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.236 Γ— 10⁹²(93-digit number)
92367828204348627189…44083997340562987521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.847 Γ— 10⁹³(94-digit number)
18473565640869725437…88167994681125975041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.694 Γ— 10⁹³(94-digit number)
36947131281739450875…76335989362251950081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.389 Γ— 10⁹³(94-digit number)
73894262563478901751…52671978724503900161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.477 Γ— 10⁹⁴(95-digit number)
14778852512695780350…05343957449007800321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.955 Γ— 10⁹⁴(95-digit number)
29557705025391560700…10687914898015600641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.911 Γ— 10⁹⁴(95-digit number)
59115410050783121401…21375829796031201281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.182 Γ— 10⁹⁡(96-digit number)
11823082010156624280…42751659592062402561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.364 Γ— 10⁹⁡(96-digit number)
23646164020313248560…85503319184124805121
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 2101855

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 532d994dfa50d361802807e0038cdfbb2c2d7ce151a3c924d409722525a33274

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 #2,101,855 on Chainz β†—
Circulating Supply:57,944,745 XPMΒ·at block #6,837,551 Β· updates every 60s
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