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Block #1,860,311

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/21/2016, 11:40:45 PM Β· Difficulty 10.6885 Β· 4,971,710 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
488b4fcb50b57fb825cc59787b8a7839dd51ef87b36dc963ce3cf6925c12c2bc
View on Chainz β†—

Difficulty

10.688479

Transactions

1

Size

200 B

Version

2

Bits

0ab04025

Nonce

455,699,383

Timestamp

11/21/2016, 11:40:45 PM

Confirmations

4,971,710

Merkle Root

204f01ff02138c658f09a33e973f98ea3ed3f635a90bccbd05804e76247c316b
Transactions (1)
Coinbase204f01ff02138c…804e76247c316b
1 in β†’ 1 out8.7400 XPM109 B
AMGX2kdD…Z2bpTK9L
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.

1.984 Γ— 10⁹⁢(97-digit number)
19840735885428415541…66053516949133255680
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
1.984 Γ— 10⁹⁢(97-digit number)
19840735885428415541…66053516949133255681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.968 Γ— 10⁹⁢(97-digit number)
39681471770856831083…32107033898266511361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.936 Γ— 10⁹⁢(97-digit number)
79362943541713662167…64214067796533022721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.587 Γ— 10⁹⁷(98-digit number)
15872588708342732433…28428135593066045441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.174 Γ— 10⁹⁷(98-digit number)
31745177416685464866…56856271186132090881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.349 Γ— 10⁹⁷(98-digit number)
63490354833370929733…13712542372264181761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.269 Γ— 10⁹⁸(99-digit number)
12698070966674185946…27425084744528363521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.539 Γ— 10⁹⁸(99-digit number)
25396141933348371893…54850169489056727041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.079 Γ— 10⁹⁸(99-digit number)
50792283866696743787…09700338978113454081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.015 Γ— 10⁹⁹(100-digit number)
10158456773339348757…19400677956226908161
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 1860311

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 488b4fcb50b57fb825cc59787b8a7839dd51ef87b36dc963ce3cf6925c12c2bc

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 #1,860,311 on Chainz β†—
Circulating Supply:57,900,298 XPMΒ·at block #6,832,020 Β· updates every 60s
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