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Home/Chain Registry/Block #2,653,691

Block #2,653,691

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/8/2018, 3:09:29 PM Β· Difficulty 11.7339 Β· 4,189,035 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6509da20ea1d8ec66c8a19b7c8910d8ba2b56090a7c4410880971e53a4b3b11a
View on Chainz β†—

Difficulty

11.733949

Transactions

1

Size

198 B

Version

2

Bits

0bbbe411

Nonce

1,580,597,872

Timestamp

5/8/2018, 3:09:29 PM

Confirmations

4,189,035

Merkle Root

3af8a460221b47a85d224ee9932d8a26bcfa9667ceb0492fbb83be7b1b0160f4
Transactions (1)
Coinbase3af8a460221b47…83be7b1b0160f4
1 in β†’ 1 out7.2500 XPM109 B
AZH9ooQs…NHUrUPcp
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.

3.088 Γ— 10⁹²(93-digit number)
30883058636719990393…18951224273164721600
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
3.088 Γ— 10⁹²(93-digit number)
30883058636719990393…18951224273164721601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.176 Γ— 10⁹²(93-digit number)
61766117273439980786…37902448546329443201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.235 Γ— 10⁹³(94-digit number)
12353223454687996157…75804897092658886401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.470 Γ— 10⁹³(94-digit number)
24706446909375992314…51609794185317772801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.941 Γ— 10⁹³(94-digit number)
49412893818751984629…03219588370635545601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.882 Γ— 10⁹³(94-digit number)
98825787637503969259…06439176741271091201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.976 Γ— 10⁹⁴(95-digit number)
19765157527500793851…12878353482542182401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.953 Γ— 10⁹⁴(95-digit number)
39530315055001587703…25756706965084364801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.906 Γ— 10⁹⁴(95-digit number)
79060630110003175407…51513413930168729601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.581 Γ— 10⁹⁡(96-digit number)
15812126022000635081…03026827860337459201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.162 Γ— 10⁹⁡(96-digit number)
31624252044001270162…06053655720674918401
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 2653691

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 6509da20ea1d8ec66c8a19b7c8910d8ba2b56090a7c4410880971e53a4b3b11a

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 #2,653,691 on Chainz β†—
Circulating Supply:57,986,147 XPMΒ·at block #6,842,725 Β· updates every 60s
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