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Block #2,086,969

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/25/2017, 9:01:25 AM Β· Difficulty 10.8737 Β· 4,756,568 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ca289950645f154884cc7d9fed76346c4c2c32d4261faadda873a9d51e67966f
View on Chainz β†—

Difficulty

10.873732

Transactions

1

Size

200 B

Version

2

Bits

0adface4

Nonce

514,184,838

Timestamp

4/25/2017, 9:01:25 AM

Confirmations

4,756,568

Merkle Root

e9b0b85a2598c7923c50875763622a977f80aaaf7b1319b8f16423978cfa0dfe
Transactions (1)
Coinbasee9b0b85a2598c7…6423978cfa0dfe
1 in β†’ 1 out8.4400 XPM110 B
AWCv6D9d…4GXcREtu
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.

1.595 Γ— 10⁹⁴(95-digit number)
15951038905216383398…36931799763196562520
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
1.595 Γ— 10⁹⁴(95-digit number)
15951038905216383398…36931799763196562521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.190 Γ— 10⁹⁴(95-digit number)
31902077810432766797…73863599526393125041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.380 Γ— 10⁹⁴(95-digit number)
63804155620865533595…47727199052786250081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.276 Γ— 10⁹⁡(96-digit number)
12760831124173106719…95454398105572500161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.552 Γ— 10⁹⁡(96-digit number)
25521662248346213438…90908796211145000321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.104 Γ— 10⁹⁡(96-digit number)
51043324496692426876…81817592422290000641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.020 Γ— 10⁹⁢(97-digit number)
10208664899338485375…63635184844580001281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.041 Γ— 10⁹⁢(97-digit number)
20417329798676970750…27270369689160002561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.083 Γ— 10⁹⁢(97-digit number)
40834659597353941500…54540739378320005121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.166 Γ— 10⁹⁢(97-digit number)
81669319194707883001…09081478756640010241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.633 Γ— 10⁹⁷(98-digit number)
16333863838941576600…18162957513280020481
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 2086969

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 ca289950645f154884cc7d9fed76346c4c2c32d4261faadda873a9d51e67966f

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 #2,086,969 on Chainz β†—
Circulating Supply:57,992,672 XPMΒ·at block #6,843,536 Β· updates every 60s
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