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Home/Chain Registry/Block #2,171,514

Block #2,171,514

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/22/2017, 3:46:25 AM Β· Difficulty 10.9056 Β· 4,670,367 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3f40c0447459bc7cbd1e775a0dfb16938f79a627ca69b2f539b78b8d97a12505
View on Chainz β†—

Difficulty

10.905624

Transactions

1

Size

200 B

Version

2

Bits

0ae7d6f2

Nonce

1,217,001,536

Timestamp

6/22/2017, 3:46:25 AM

Confirmations

4,670,367

Merkle Root

2efaee1e0a8cf9b33c76602cd659f5718cc72f132d2c18afef517119d2bc748a
Transactions (1)
Coinbase2efaee1e0a8cf9…517119d2bc748a
1 in β†’ 1 out8.3900 XPM109 B
APEM4RjH…QfrTXJXr
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.

5.706 Γ— 10⁹⁢(97-digit number)
57066900491527612306…36136696489607024640
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
5.706 Γ— 10⁹⁢(97-digit number)
57066900491527612306…36136696489607024641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.141 Γ— 10⁹⁷(98-digit number)
11413380098305522461…72273392979214049281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.282 Γ— 10⁹⁷(98-digit number)
22826760196611044922…44546785958428098561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.565 Γ— 10⁹⁷(98-digit number)
45653520393222089844…89093571916856197121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.130 Γ— 10⁹⁷(98-digit number)
91307040786444179689…78187143833712394241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.826 Γ— 10⁹⁸(99-digit number)
18261408157288835937…56374287667424788481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.652 Γ— 10⁹⁸(99-digit number)
36522816314577671875…12748575334849576961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.304 Γ— 10⁹⁸(99-digit number)
73045632629155343751…25497150669699153921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.460 Γ— 10⁹⁹(100-digit number)
14609126525831068750…50994301339398307841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.921 Γ— 10⁹⁹(100-digit number)
29218253051662137500…01988602678796615681
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 2171514

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 3f40c0447459bc7cbd1e775a0dfb16938f79a627ca69b2f539b78b8d97a12505

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 #2,171,514 on Chainz β†—
Circulating Supply:57,979,423 XPMΒ·at block #6,841,880 Β· updates every 60s
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