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Home/Chain Registry/Block #3,048,997

Block #3,048,997

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/11/2019, 11:42:06 PM Β· Difficulty 10.9961 Β· 3,788,075 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d65d497d13a6313e4a4cf887eef5388758e58b37714f2e4a11e5095df1aae216
View on Chainz β†—

Difficulty

10.996078

Transactions

1

Size

200 B

Version

2

Bits

0afefefc

Nonce

29,621,127

Timestamp

2/11/2019, 11:42:06 PM

Confirmations

3,788,075

Merkle Root

4edcb811038214c53082edd4831e24984d740f2723e6351c7145c245eef689e5
Transactions (1)
Coinbase4edcb811038214…45c245eef689e5
1 in β†’ 1 out8.2600 XPM110 B
AUMQRepm…tAfKmdW1
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.

4.365 Γ— 10⁹⁡(96-digit number)
43655893330847156425…64211549470126364160
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
4.365 Γ— 10⁹⁡(96-digit number)
43655893330847156425…64211549470126364161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.731 Γ— 10⁹⁡(96-digit number)
87311786661694312851…28423098940252728321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.746 Γ— 10⁹⁢(97-digit number)
17462357332338862570…56846197880505456641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.492 Γ— 10⁹⁢(97-digit number)
34924714664677725140…13692395761010913281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.984 Γ— 10⁹⁢(97-digit number)
69849429329355450281…27384791522021826561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.396 Γ— 10⁹⁷(98-digit number)
13969885865871090056…54769583044043653121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.793 Γ— 10⁹⁷(98-digit number)
27939771731742180112…09539166088087306241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.587 Γ— 10⁹⁷(98-digit number)
55879543463484360225…19078332176174612481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.117 Γ— 10⁹⁸(99-digit number)
11175908692696872045…38156664352349224961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.235 Γ— 10⁹⁸(99-digit number)
22351817385393744090…76313328704698449921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.470 Γ— 10⁹⁸(99-digit number)
44703634770787488180…52626657409396899841
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 3048997

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 d65d497d13a6313e4a4cf887eef5388758e58b37714f2e4a11e5095df1aae216

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 #3,048,997 on Chainz β†—
Circulating Supply:57,940,881 XPMΒ·at block #6,837,071 Β· updates every 60s
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