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Home/Chain Registry/Block #2,617,637

Block #2,617,637

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/17/2018, 7:17:04 AM Β· Difficulty 11.2296 Β· 4,195,191 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
157ec285ce27baa74067e1c54e80571ce5ef847d6909ab478576ed8cfce84c76
View on Chainz β†—

Difficulty

11.229649

Transactions

1

Size

199 B

Version

2

Bits

0b3aca4a

Nonce

986,432,712

Timestamp

4/17/2018, 7:17:04 AM

Confirmations

4,195,191

Merkle Root

0536f4bbd88f8c5ee172959f7dc1ca299330564a2f6e54e93b7c228e4fc9fdcb
Transactions (1)
Coinbase0536f4bbd88f8c…7c228e4fc9fdcb
1 in β†’ 1 out7.9200 XPM110 B
AafVYRnt…cNv4CdP3
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.

1.393 Γ— 10⁹³(94-digit number)
13939764741403925234…88073273773430062850
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
1.393 Γ— 10⁹³(94-digit number)
13939764741403925234…88073273773430062851
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.787 Γ— 10⁹³(94-digit number)
27879529482807850468…76146547546860125701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.575 Γ— 10⁹³(94-digit number)
55759058965615700936…52293095093720251401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.115 Γ— 10⁹⁴(95-digit number)
11151811793123140187…04586190187440502801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.230 Γ— 10⁹⁴(95-digit number)
22303623586246280374…09172380374881005601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.460 Γ— 10⁹⁴(95-digit number)
44607247172492560748…18344760749762011201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.921 Γ— 10⁹⁴(95-digit number)
89214494344985121497…36689521499524022401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.784 Γ— 10⁹⁡(96-digit number)
17842898868997024299…73379042999048044801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.568 Γ— 10⁹⁡(96-digit number)
35685797737994048599…46758085998096089601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.137 Γ— 10⁹⁡(96-digit number)
71371595475988097198…93516171996192179201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.427 Γ— 10⁹⁢(97-digit number)
14274319095197619439…87032343992384358401
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 2617637

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 157ec285ce27baa74067e1c54e80571ce5ef847d6909ab478576ed8cfce84c76

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 #2,617,637 on Chainz β†—
Circulating Supply:57,746,671 XPMΒ·at block #6,812,827 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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