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Block #636,256

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2014, 7:08:07 PM Β· Difficulty 10.9639 Β· 6,189,964 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f775e5b1dab97476bd622a16681d70c6d9ea03286dfa4e5a38800e9c6aa51f36
View on Chainz β†—

Height

#636,256

Difficulty

10.963878

Transactions

2

Size

432 B

Version

2

Bits

0af6c0ae

Nonce

9,510,990

Timestamp

7/16/2014, 7:08:07 PM

Confirmations

6,189,964

Merkle Root

470e709d8c7d576e22dfedf8c30d1791e828de33e1546de09292462df159d6bc
Transactions (2)
Coinbase5acaab327489e3…e75f415f57c41c
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
9aa71e5c65ae34…874200f558c2d3
1 in β†’ 2 out6.1017 XPM226 B
AazUh71S…khF8RgqSAe7ht6Sj…7i8cq412
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.

2.081 Γ— 10⁹⁴(95-digit number)
20818270174074456120…95300318052597149440
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.081 Γ— 10⁹⁴(95-digit number)
20818270174074456120…95300318052597149439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.163 Γ— 10⁹⁴(95-digit number)
41636540348148912240…90600636105194298879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.327 Γ— 10⁹⁴(95-digit number)
83273080696297824480…81201272210388597759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.665 Γ— 10⁹⁡(96-digit number)
16654616139259564896…62402544420777195519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.330 Γ— 10⁹⁡(96-digit number)
33309232278519129792…24805088841554391039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.661 Γ— 10⁹⁡(96-digit number)
66618464557038259584…49610177683108782079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.332 Γ— 10⁹⁢(97-digit number)
13323692911407651916…99220355366217564159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.664 Γ— 10⁹⁢(97-digit number)
26647385822815303833…98440710732435128319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.329 Γ— 10⁹⁢(97-digit number)
53294771645630607667…96881421464870256639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.065 Γ— 10⁹⁷(98-digit number)
10658954329126121533…93762842929740513279
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 636256

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 f775e5b1dab97476bd622a16681d70c6d9ea03286dfa4e5a38800e9c6aa51f36

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 #636,256 on Chainz β†—
Circulating Supply:57,853,893 XPMΒ·at block #6,826,219 Β· updates every 60s
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