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Home/Chain Registry/Block #2,726,968

Block #2,726,968

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/29/2018, 5:16:05 PM Β· Difficulty 11.6276 Β· 4,116,367 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
73b581b8a3f91e8dc69983ccb6c4c874300418b620de228e5185ea8b7b2c60ed
View on Chainz β†—

Difficulty

11.627612

Transactions

1

Size

200 B

Version

2

Bits

0ba0ab31

Nonce

1,098,578,084

Timestamp

6/29/2018, 5:16:05 PM

Confirmations

4,116,367

Merkle Root

3baff7bcb0e1754957823b2ffbb75b69628709f4b18b63065b3b2153fe9833b3
Transactions (1)
Coinbase3baff7bcb0e175…3b2153fe9833b3
1 in β†’ 1 out7.3800 XPM110 B
AZtxQr2F…7grUWrUz
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.

5.527 Γ— 10⁹⁡(96-digit number)
55273559379816434806…38025968652475824640
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
5.527 Γ— 10⁹⁡(96-digit number)
55273559379816434806…38025968652475824641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.105 Γ— 10⁹⁢(97-digit number)
11054711875963286961…76051937304951649281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.210 Γ— 10⁹⁢(97-digit number)
22109423751926573922…52103874609903298561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.421 Γ— 10⁹⁢(97-digit number)
44218847503853147844…04207749219806597121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.843 Γ— 10⁹⁢(97-digit number)
88437695007706295689…08415498439613194241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.768 Γ— 10⁹⁷(98-digit number)
17687539001541259137…16830996879226388481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.537 Γ— 10⁹⁷(98-digit number)
35375078003082518275…33661993758452776961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.075 Γ— 10⁹⁷(98-digit number)
70750156006165036551…67323987516905553921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.415 Γ— 10⁹⁸(99-digit number)
14150031201233007310…34647975033811107841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.830 Γ— 10⁹⁸(99-digit number)
28300062402466014620…69295950067622215681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.660 Γ— 10⁹⁸(99-digit number)
56600124804932029241…38591900135244431361
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 2726968

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 73b581b8a3f91e8dc69983ccb6c4c874300418b620de228e5185ea8b7b2c60ed

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 #2,726,968 on Chainz β†—
Circulating Supply:57,991,042 XPMΒ·at block #6,843,334 Β· updates every 60s
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