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Block #900,536

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/18/2015, 9:10:14 PM Β· Difficulty 10.9426 Β· 5,917,163 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c40dc2a9d9d183a2df94ba400bfddc6eadcc25c817e164c76e48da2ee4b78b73
View on Chainz β†—

Height

#900,536

Difficulty

10.942609

Transactions

1

Size

207 B

Version

2

Bits

0af14ece

Nonce

331,992,785

Timestamp

1/18/2015, 9:10:14 PM

Confirmations

5,917,163

Merkle Root

ddba7615f84f69a08d2acd272f09faf85412a84cce0fbd79a823dd0a6021247e
Transactions (1)
Coinbaseddba7615f84f69…23dd0a6021247e
1 in β†’ 1 out8.3400 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.

9.165 Γ— 10⁹⁢(97-digit number)
91656605966971195933…57610985030151740160
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
9.165 Γ— 10⁹⁢(97-digit number)
91656605966971195933…57610985030151740159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.833 Γ— 10⁹⁷(98-digit number)
18331321193394239186…15221970060303480319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.666 Γ— 10⁹⁷(98-digit number)
36662642386788478373…30443940120606960639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.332 Γ— 10⁹⁷(98-digit number)
73325284773576956747…60887880241213921279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.466 Γ— 10⁹⁸(99-digit number)
14665056954715391349…21775760482427842559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.933 Γ— 10⁹⁸(99-digit number)
29330113909430782698…43551520964855685119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.866 Γ— 10⁹⁸(99-digit number)
58660227818861565397…87103041929711370239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.173 Γ— 10⁹⁹(100-digit number)
11732045563772313079…74206083859422740479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.346 Γ— 10⁹⁹(100-digit number)
23464091127544626159…48412167718845480959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.692 Γ— 10⁹⁹(100-digit number)
46928182255089252318…96824335437690961919
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 900536

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 c40dc2a9d9d183a2df94ba400bfddc6eadcc25c817e164c76e48da2ee4b78b73

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 #900,536 on Chainz β†—
Circulating Supply:57,785,651 XPMΒ·at block #6,817,698 Β· updates every 60s
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