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Home/Chain Registry/Block #2,756,903

Block #2,756,903

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2018, 3:27:07 AM Β· Difficulty 11.6654 Β· 4,085,805 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1e2076a48e4e1c418dc1b88dfb6b68d7632b4fd35bff880ef5acd505c0e60734
View on Chainz β†—

Difficulty

11.665413

Transactions

1

Size

201 B

Version

2

Bits

0baa587a

Nonce

1,800,381,777

Timestamp

7/20/2018, 3:27:07 AM

Confirmations

4,085,805

Merkle Root

7deeef04820d0c7539a7c2ab607f5c361a0d64fbd73a7cbd7cd613a77f8ef90f
Transactions (1)
Coinbase7deeef04820d0c…d613a77f8ef90f
1 in β†’ 1 out7.3400 XPM110 B
AWirsx16…37pJsemz
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.

5.999 Γ— 10⁹⁷(98-digit number)
59991900421669067176…93240699369215877120
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
5.999 Γ— 10⁹⁷(98-digit number)
59991900421669067176…93240699369215877121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.199 Γ— 10⁹⁸(99-digit number)
11998380084333813435…86481398738431754241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.399 Γ— 10⁹⁸(99-digit number)
23996760168667626870…72962797476863508481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.799 Γ— 10⁹⁸(99-digit number)
47993520337335253741…45925594953727016961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.598 Γ— 10⁹⁸(99-digit number)
95987040674670507482…91851189907454033921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.919 Γ— 10⁹⁹(100-digit number)
19197408134934101496…83702379814908067841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.839 Γ— 10⁹⁹(100-digit number)
38394816269868202993…67404759629816135681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.678 Γ— 10⁹⁹(100-digit number)
76789632539736405986…34809519259632271361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.535 Γ— 10¹⁰⁰(101-digit number)
15357926507947281197…69619038519264542721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.071 Γ— 10¹⁰⁰(101-digit number)
30715853015894562394…39238077038529085441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.143 Γ— 10¹⁰⁰(101-digit number)
61431706031789124789…78476154077058170881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.228 Γ— 10¹⁰¹(102-digit number)
12286341206357824957…56952308154116341761
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 2756903

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 1e2076a48e4e1c418dc1b88dfb6b68d7632b4fd35bff880ef5acd505c0e60734

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 #2,756,903 on Chainz β†—
Circulating Supply:57,986,002 XPMΒ·at block #6,842,707 Β· updates every 60s
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