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Home/Chain Registry/Block #2,637,812

Block #2,637,812

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 1:37:59 AM Β· Difficulty 11.4609 Β· 4,207,803 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0815c888ce4b9988d9ae1159f222076c6872df46e1f761efb5171e51c0839632
View on Chainz β†—

Difficulty

11.460885

Transactions

1

Size

200 B

Version

2

Bits

0b75fc8a

Nonce

453,258,597

Timestamp

4/30/2018, 1:37:59 AM

Confirmations

4,207,803

Merkle Root

13edcb9bbd626a34d6971ed9569da3661d46813b2c374837dfdb64276145aee3
Transactions (1)
Coinbase13edcb9bbd626a…db64276145aee3
1 in β†’ 1 out7.6000 XPM110 B
Adqah8zh…1WwoHJ9t
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.

5.940 Γ— 10⁹³(94-digit number)
59400871992638105223…19179428701769037160
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
5.940 Γ— 10⁹³(94-digit number)
59400871992638105223…19179428701769037161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.188 Γ— 10⁹⁴(95-digit number)
11880174398527621044…38358857403538074321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.376 Γ— 10⁹⁴(95-digit number)
23760348797055242089…76717714807076148641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.752 Γ— 10⁹⁴(95-digit number)
47520697594110484178…53435429614152297281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.504 Γ— 10⁹⁴(95-digit number)
95041395188220968357…06870859228304594561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.900 Γ— 10⁹⁡(96-digit number)
19008279037644193671…13741718456609189121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.801 Γ— 10⁹⁡(96-digit number)
38016558075288387342…27483436913218378241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.603 Γ— 10⁹⁡(96-digit number)
76033116150576774685…54966873826436756481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.520 Γ— 10⁹⁢(97-digit number)
15206623230115354937…09933747652873512961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.041 Γ— 10⁹⁢(97-digit number)
30413246460230709874…19867495305747025921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.082 Γ— 10⁹⁢(97-digit number)
60826492920461419748…39734990611494051841
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 2637812

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 0815c888ce4b9988d9ae1159f222076c6872df46e1f761efb5171e51c0839632

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 #2,637,812 on Chainz β†—
Circulating Supply:58,009,369 XPMΒ·at block #6,845,614 Β· updates every 60s
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