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Block #636,263

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2014, 7:13:41 PM Β· Difficulty 10.9639 Β· 6,190,271 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a56c4d64081a135adf8661aae3ef552dd51fad917a7d52732bb76abce7deb9b0
View on Chainz β†—

Height

#636,263

Difficulty

10.963888

Transactions

2

Size

432 B

Version

2

Bits

0af6c165

Nonce

1,347,651,101

Timestamp

7/16/2014, 7:13:41 PM

Confirmations

6,190,271

Merkle Root

d36e14f51f5a4b14e466cd887d837856a6bedd2e333d6d18cdf7c7e7fcef5f59
Transactions (2)
Coinbase23f04b64e2db8f…e4adb360575c79
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
82056d8f4ab344…b7f5e7e5700842
1 in β†’ 2 out7.2689 XPM225 B
AaCbF1V4…UYQWaEAZAS9ZCvju…bu3NEFwZ
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.

1.508 Γ— 10⁹⁢(97-digit number)
15088816385167093411…55584529900320541400
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
1.508 Γ— 10⁹⁢(97-digit number)
15088816385167093411…55584529900320541401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.017 Γ— 10⁹⁢(97-digit number)
30177632770334186823…11169059800641082801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.035 Γ— 10⁹⁢(97-digit number)
60355265540668373646…22338119601282165601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.207 Γ— 10⁹⁷(98-digit number)
12071053108133674729…44676239202564331201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.414 Γ— 10⁹⁷(98-digit number)
24142106216267349458…89352478405128662401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.828 Γ— 10⁹⁷(98-digit number)
48284212432534698917…78704956810257324801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.656 Γ— 10⁹⁷(98-digit number)
96568424865069397834…57409913620514649601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.931 Γ— 10⁹⁸(99-digit number)
19313684973013879566…14819827241029299201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.862 Γ— 10⁹⁸(99-digit number)
38627369946027759133…29639654482058598401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.725 Γ— 10⁹⁸(99-digit number)
77254739892055518267…59279308964117196801
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 636263

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 a56c4d64081a135adf8661aae3ef552dd51fad917a7d52732bb76abce7deb9b0

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 #636,263 on Chainz β†—
Circulating Supply:57,856,419 XPMΒ·at block #6,826,533 Β· updates every 60s
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