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Block #2,121,527

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/18/2017, 1:54:41 AM Β· Difficulty 10.9136 Β· 4,709,911 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b1f17d1b1770aacce81c891055bf12d040f380526796b6786cbf9662584323d1
View on Chainz β†—

Difficulty

10.913599

Transactions

1

Size

199 B

Version

2

Bits

0ae9e1a3

Nonce

499,325,934

Timestamp

5/18/2017, 1:54:41 AM

Confirmations

4,709,911

Merkle Root

0da33736da0cd9ed1784e5dc95371cc9ba0be856bc47b7c5a5e981a94f48e01c
Transactions (1)
Coinbase0da33736da0cd9…e981a94f48e01c
1 in β†’ 1 out8.3800 XPM109 B
AFtQ4cFK…ik366v9g
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.

3.067 Γ— 10⁹⁡(96-digit number)
30673305829206488473…73969561621364769280
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
3.067 Γ— 10⁹⁡(96-digit number)
30673305829206488473…73969561621364769281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.134 Γ— 10⁹⁡(96-digit number)
61346611658412976947…47939123242729538561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.226 Γ— 10⁹⁢(97-digit number)
12269322331682595389…95878246485459077121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.453 Γ— 10⁹⁢(97-digit number)
24538644663365190778…91756492970918154241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.907 Γ— 10⁹⁢(97-digit number)
49077289326730381557…83512985941836308481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.815 Γ— 10⁹⁢(97-digit number)
98154578653460763115…67025971883672616961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.963 Γ— 10⁹⁷(98-digit number)
19630915730692152623…34051943767345233921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.926 Γ— 10⁹⁷(98-digit number)
39261831461384305246…68103887534690467841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.852 Γ— 10⁹⁷(98-digit number)
78523662922768610492…36207775069380935681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.570 Γ— 10⁹⁸(99-digit number)
15704732584553722098…72415550138761871361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.140 Γ— 10⁹⁸(99-digit number)
31409465169107444196…44831100277523742721
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2121527

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 b1f17d1b1770aacce81c891055bf12d040f380526796b6786cbf9662584323d1

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 #2,121,527 on Chainz β†—
Circulating Supply:57,895,667 XPMΒ·at block #6,831,437 Β· updates every 60s
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