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Block #862,096

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/21/2014, 11:44:06 AM Β· Difficulty 10.9637 Β· 5,968,316 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
91ed8e86952095dc9d29ec0b426c70d4dc9349dbf34eed22a80964128475829c
View on Chainz β†—

Height

#862,096

Difficulty

10.963655

Transactions

1

Size

206 B

Version

2

Bits

0af6b220

Nonce

894,253,541

Timestamp

12/21/2014, 11:44:06 AM

Confirmations

5,968,316

Merkle Root

4f63f61ade4553e43438f5195cad37a1637b2cbf65b6e32a6a21515777865b48
Transactions (1)
Coinbase4f63f61ade4553…21515777865b48
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.707 Γ— 10⁹⁴(95-digit number)
27073450061410904794…75255613104206178960
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
2.707 Γ— 10⁹⁴(95-digit number)
27073450061410904794…75255613104206178961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.414 Γ— 10⁹⁴(95-digit number)
54146900122821809588…50511226208412357921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.082 Γ— 10⁹⁡(96-digit number)
10829380024564361917…01022452416824715841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.165 Γ— 10⁹⁡(96-digit number)
21658760049128723835…02044904833649431681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.331 Γ— 10⁹⁡(96-digit number)
43317520098257447670…04089809667298863361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.663 Γ— 10⁹⁡(96-digit number)
86635040196514895341…08179619334597726721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.732 Γ— 10⁹⁢(97-digit number)
17327008039302979068…16359238669195453441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.465 Γ— 10⁹⁢(97-digit number)
34654016078605958136…32718477338390906881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.930 Γ— 10⁹⁢(97-digit number)
69308032157211916273…65436954676781813761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.386 Γ— 10⁹⁷(98-digit number)
13861606431442383254…30873909353563627521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.772 Γ— 10⁹⁷(98-digit number)
27723212862884766509…61747818707127255041
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 862096

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 91ed8e86952095dc9d29ec0b426c70d4dc9349dbf34eed22a80964128475829c

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 #862,096 on Chainz β†—
Circulating Supply:57,887,536 XPMΒ·at block #6,830,411 Β· updates every 60s
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