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Block #285,678

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/30/2013, 2:19:37 PM Β· Difficulty 9.9846 Β· 6,518,319 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4775ef86c7817277c0bb51f33f13576caad94f05802f6f5d6459495d20742f21
View on Chainz β†—

Height

#285,678

Difficulty

9.984619

Transactions

1

Size

206 B

Version

2

Bits

09fc1002

Nonce

2,529

Timestamp

11/30/2013, 2:19:37 PM

Confirmations

6,518,319

Merkle Root

2f9df7ab76732cd8e2c4a7e87fd1651585d94c9a2261214ec8d8ff0494440994
Transactions (1)
Coinbase2f9df7ab76732c…d8ff0494440994
1 in β†’ 1 out10.0200 XPM116 B
AcLBm5Z9…S683d7c3
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.

5.983 Γ— 10⁹⁴(95-digit number)
59834916907317737647…55753485868255907840
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
5.983 Γ— 10⁹⁴(95-digit number)
59834916907317737647…55753485868255907841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.196 Γ— 10⁹⁡(96-digit number)
11966983381463547529…11506971736511815681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.393 Γ— 10⁹⁡(96-digit number)
23933966762927095059…23013943473023631361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.786 Γ— 10⁹⁡(96-digit number)
47867933525854190118…46027886946047262721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.573 Γ— 10⁹⁡(96-digit number)
95735867051708380236…92055773892094525441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.914 Γ— 10⁹⁢(97-digit number)
19147173410341676047…84111547784189050881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.829 Γ— 10⁹⁢(97-digit number)
38294346820683352094…68223095568378101761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.658 Γ— 10⁹⁢(97-digit number)
76588693641366704189…36446191136756203521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.531 Γ— 10⁹⁷(98-digit number)
15317738728273340837…72892382273512407041
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 285678

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 4775ef86c7817277c0bb51f33f13576caad94f05802f6f5d6459495d20742f21

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 #285,678 on Chainz β†—
Circulating Supply:57,676,024 XPMΒ·at block #6,803,996 Β· updates every 60s
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