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Block #2,759,860

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/22/2018, 6:23:09 AM Β· Difficulty 11.6589 Β· 4,084,847 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fc1a88b7e72897c4841b708c6aed7f0838c976dad0836d25138f22781680784d
View on Chainz β†—

Difficulty

11.658875

Transactions

1

Size

200 B

Version

2

Bits

0ba8ac01

Nonce

81,381,741

Timestamp

7/22/2018, 6:23:09 AM

Confirmations

4,084,847

Merkle Root

b15829d85c8d6f712275b4d284dd287b08b6e73d0a52775392e9a4536da3c1c9
Transactions (1)
Coinbaseb15829d85c8d6f…e9a4536da3c1c9
1 in β†’ 1 out7.3400 XPM110 B
Ad4uEPc5…DSPCxoQ8
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.

2.104 Γ— 10⁹⁡(96-digit number)
21040150973024734520…03500141781766231680
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
2.104 Γ— 10⁹⁡(96-digit number)
21040150973024734520…03500141781766231681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.208 Γ— 10⁹⁡(96-digit number)
42080301946049469040…07000283563532463361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.416 Γ— 10⁹⁡(96-digit number)
84160603892098938080…14000567127064926721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.683 Γ— 10⁹⁢(97-digit number)
16832120778419787616…28001134254129853441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.366 Γ— 10⁹⁢(97-digit number)
33664241556839575232…56002268508259706881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.732 Γ— 10⁹⁢(97-digit number)
67328483113679150464…12004537016519413761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.346 Γ— 10⁹⁷(98-digit number)
13465696622735830092…24009074033038827521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.693 Γ— 10⁹⁷(98-digit number)
26931393245471660185…48018148066077655041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.386 Γ— 10⁹⁷(98-digit number)
53862786490943320371…96036296132155310081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.077 Γ— 10⁹⁸(99-digit number)
10772557298188664074…92072592264310620161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.154 Γ— 10⁹⁸(99-digit number)
21545114596377328148…84145184528621240321
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 2759860

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 fc1a88b7e72897c4841b708c6aed7f0838c976dad0836d25138f22781680784d

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 #2,759,860 on Chainz β†—
Circulating Supply:58,002,066 XPMΒ·at block #6,844,706 Β· updates every 60s
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