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Home/Chain Registry/Block #845,985

Block #845,985

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/9/2014, 6:53:40 AM Β· Difficulty 10.9724 Β· 5,997,844 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
018a272ed8bab788ae038be71fa1f21489e44112d5f591ff0709b65a40c8c39e
View on Chainz β†—

Height

#845,985

Difficulty

10.972354

Transactions

2

Size

433 B

Version

2

Bits

0af8ec36

Nonce

1,125,075,571

Timestamp

12/9/2014, 6:53:40 AM

Confirmations

5,997,844

Merkle Root

57a9c601d829c87897f15e6a2473c7b13dfe287d80a44fa35d09e6fed48e6590
Transactions (2)
Coinbased75f7f82591476…6ef775eb504e6e
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
2641db92c5e2e2…5f072ba609c921
1 in β†’ 2 out0.1457 XPM226 B
AQujXFKW…FFUZ3jgqAe7mPVTk…YWX63EmP
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.

1.280 Γ— 10⁹⁷(98-digit number)
12808662995790170936…82221654701889756160
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
1.280 Γ— 10⁹⁷(98-digit number)
12808662995790170936…82221654701889756161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.561 Γ— 10⁹⁷(98-digit number)
25617325991580341872…64443309403779512321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.123 Γ— 10⁹⁷(98-digit number)
51234651983160683744…28886618807559024641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.024 Γ— 10⁹⁸(99-digit number)
10246930396632136748…57773237615118049281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.049 Γ— 10⁹⁸(99-digit number)
20493860793264273497…15546475230236098561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.098 Γ— 10⁹⁸(99-digit number)
40987721586528546995…31092950460472197121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.197 Γ— 10⁹⁸(99-digit number)
81975443173057093991…62185900920944394241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.639 Γ— 10⁹⁹(100-digit number)
16395088634611418798…24371801841888788481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.279 Γ— 10⁹⁹(100-digit number)
32790177269222837596…48743603683777576961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.558 Γ— 10⁹⁹(100-digit number)
65580354538445675193…97487207367555153921
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 845985

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 018a272ed8bab788ae038be71fa1f21489e44112d5f591ff0709b65a40c8c39e

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 #845,985 on Chainz β†—
Circulating Supply:57,995,008 XPMΒ·at block #6,843,828 Β· updates every 60s
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