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Home/Chain Registry/Block #560,985

Block #560,985

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2014, 5:31:22 AM Β· Difficulty 10.9650 Β· 6,251,156 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a3e50c8a58b0760b1903725be53bf3f8ee2c4b2a0ab4676dfb917ca71ec5713c
View on Chainz β†—

Height

#560,985

Difficulty

10.964964

Transactions

1

Size

207 B

Version

2

Bits

0af707dc

Nonce

262,305,654

Timestamp

5/25/2014, 5:31:22 AM

Confirmations

6,251,156

Merkle Root

b6dff6b5e73173c8104a862b2f7e96db3a13861e6e491f2973ebe79b6e18af71
Transactions (1)
Coinbaseb6dff6b5e73173…ebe79b6e18af71
1 in β†’ 1 out8.3000 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.

6.006 Γ— 10⁹⁢(97-digit number)
60061582238542105031…26514540086133130800
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
6.006 Γ— 10⁹⁢(97-digit number)
60061582238542105031…26514540086133130801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.201 Γ— 10⁹⁷(98-digit number)
12012316447708421006…53029080172266261601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.402 Γ— 10⁹⁷(98-digit number)
24024632895416842012…06058160344532523201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.804 Γ— 10⁹⁷(98-digit number)
48049265790833684024…12116320689065046401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.609 Γ— 10⁹⁷(98-digit number)
96098531581667368049…24232641378130092801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.921 Γ— 10⁹⁸(99-digit number)
19219706316333473609…48465282756260185601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.843 Γ— 10⁹⁸(99-digit number)
38439412632666947219…96930565512520371201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.687 Γ— 10⁹⁸(99-digit number)
76878825265333894439…93861131025040742401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.537 Γ— 10⁹⁹(100-digit number)
15375765053066778887…87722262050081484801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.075 Γ— 10⁹⁹(100-digit number)
30751530106133557775…75444524100162969601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.150 Γ— 10⁹⁹(100-digit number)
61503060212267115551…50889048200325939201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 560985

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 a3e50c8a58b0760b1903725be53bf3f8ee2c4b2a0ab4676dfb917ca71ec5713c

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 #560,985 on Chainz β†—
Circulating Supply:57,741,143 XPMΒ·at block #6,812,140 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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