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Home/Chain Registry/Block #2,580,271

Block #2,580,271

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/23/2018, 3:08:48 AM Β· Difficulty 11.0364 Β· 4,260,639 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d522ec837334e03bc9101e0f061bf413807b9c5458888973edfa7a7697668d1d
View on Chainz β†—

Difficulty

11.036387

Transactions

1

Size

199 B

Version

2

Bits

0b0950aa

Nonce

710,412,955

Timestamp

3/23/2018, 3:08:48 AM

Confirmations

4,260,639

Merkle Root

edced934a74daad7cf4e17e642a67751363a469e2ce5f4f4111ad9100e6a8584
Transactions (1)
Coinbaseedced934a74daa…1ad9100e6a8584
1 in β†’ 1 out8.2000 XPM109 B
ALQGpaT6…9dLVU1B9
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.

3.987 Γ— 10⁹⁴(95-digit number)
39870838356566904866…97182765318699376640
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
3.987 Γ— 10⁹⁴(95-digit number)
39870838356566904866…97182765318699376641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.974 Γ— 10⁹⁴(95-digit number)
79741676713133809732…94365530637398753281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.594 Γ— 10⁹⁡(96-digit number)
15948335342626761946…88731061274797506561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.189 Γ— 10⁹⁡(96-digit number)
31896670685253523892…77462122549595013121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.379 Γ— 10⁹⁡(96-digit number)
63793341370507047785…54924245099190026241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.275 Γ— 10⁹⁢(97-digit number)
12758668274101409557…09848490198380052481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.551 Γ— 10⁹⁢(97-digit number)
25517336548202819114…19696980396760104961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.103 Γ— 10⁹⁢(97-digit number)
51034673096405638228…39393960793520209921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.020 Γ— 10⁹⁷(98-digit number)
10206934619281127645…78787921587040419841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.041 Γ— 10⁹⁷(98-digit number)
20413869238562255291…57575843174080839681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.082 Γ— 10⁹⁷(98-digit number)
40827738477124510582…15151686348161679361
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 2580271

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 d522ec837334e03bc9101e0f061bf413807b9c5458888973edfa7a7697668d1d

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 #2,580,271 on Chainz β†—
Circulating Supply:57,971,631 XPMΒ·at block #6,840,909 Β· updates every 60s
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