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Home/Chain Registry/Block #2,114,518

Block #2,114,518

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/13/2017, 4:58:42 PM Β· Difficulty 10.9002 Β· 4,718,597 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a6be49ed00749565f22b976993418fb3285b274b730043ea01b1f36277dda2ca
View on Chainz β†—

Difficulty

10.900226

Transactions

1

Size

199 B

Version

2

Bits

0ae67531

Nonce

7,056,664

Timestamp

5/13/2017, 4:58:42 PM

Confirmations

4,718,597

Merkle Root

dbe18aa8d1ee2996e7da8ed3038aaa21f00591f5f2f6fd01b90a1cb49d3c7285
Transactions (1)
Coinbasedbe18aa8d1ee29…0a1cb49d3c7285
1 in β†’ 1 out8.4000 XPM109 B
AQnfiePe…tDzECbV1
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.

4.666 Γ— 10⁹⁴(95-digit number)
46662738762065411039…48287555371129246400
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
4.666 Γ— 10⁹⁴(95-digit number)
46662738762065411039…48287555371129246401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.332 Γ— 10⁹⁴(95-digit number)
93325477524130822078…96575110742258492801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.866 Γ— 10⁹⁡(96-digit number)
18665095504826164415…93150221484516985601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.733 Γ— 10⁹⁡(96-digit number)
37330191009652328831…86300442969033971201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.466 Γ— 10⁹⁡(96-digit number)
74660382019304657662…72600885938067942401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.493 Γ— 10⁹⁢(97-digit number)
14932076403860931532…45201771876135884801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.986 Γ— 10⁹⁢(97-digit number)
29864152807721863065…90403543752271769601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.972 Γ— 10⁹⁢(97-digit number)
59728305615443726130…80807087504543539201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.194 Γ— 10⁹⁷(98-digit number)
11945661123088745226…61614175009087078401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.389 Γ— 10⁹⁷(98-digit number)
23891322246177490452…23228350018174156801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.778 Γ— 10⁹⁷(98-digit number)
47782644492354980904…46456700036348313601
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 2114518

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 a6be49ed00749565f22b976993418fb3285b274b730043ea01b1f36277dda2ca

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 #2,114,518 on Chainz β†—
Circulating Supply:57,909,095 XPMΒ·at block #6,833,114 Β· updates every 60s
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