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Home/Chain Registry/Block #2,038,870

Block #2,038,870

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/26/2017, 3:57:03 AM Β· Difficulty 10.6808 Β· 4,803,112 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dd3eab0e9bc921f025b4afd44b4f58336daa00c9bcfb0ad34ea9e0fa34aae6b5
View on Chainz β†—

Difficulty

10.680781

Transactions

1

Size

199 B

Version

2

Bits

0aae47ac

Nonce

520,475,631

Timestamp

3/26/2017, 3:57:03 AM

Confirmations

4,803,112

Merkle Root

432b85da3b21d99e59ea434188d37cd382ffb5ca83c034a8ea94e9e2468f2362
Transactions (1)
Coinbase432b85da3b21d9…94e9e2468f2362
1 in β†’ 1 out8.7500 XPM109 B
AVGH14Gb…5hJMdHu8
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.

2.001 Γ— 10⁹⁡(96-digit number)
20010450353400888835…94726278186503416960
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
2.001 Γ— 10⁹⁡(96-digit number)
20010450353400888835…94726278186503416961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.002 Γ— 10⁹⁡(96-digit number)
40020900706801777671…89452556373006833921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.004 Γ— 10⁹⁡(96-digit number)
80041801413603555342…78905112746013667841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.600 Γ— 10⁹⁢(97-digit number)
16008360282720711068…57810225492027335681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.201 Γ— 10⁹⁢(97-digit number)
32016720565441422136…15620450984054671361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.403 Γ— 10⁹⁢(97-digit number)
64033441130882844273…31240901968109342721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.280 Γ— 10⁹⁷(98-digit number)
12806688226176568854…62481803936218685441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.561 Γ— 10⁹⁷(98-digit number)
25613376452353137709…24963607872437370881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.122 Γ— 10⁹⁷(98-digit number)
51226752904706275418…49927215744874741761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.024 Γ— 10⁹⁸(99-digit number)
10245350580941255083…99854431489749483521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.049 Γ— 10⁹⁸(99-digit number)
20490701161882510167…99708862979498967041
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 2038870

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 dd3eab0e9bc921f025b4afd44b4f58336daa00c9bcfb0ad34ea9e0fa34aae6b5

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 #2,038,870 on Chainz β†—
Circulating Supply:57,980,241 XPMΒ·at block #6,841,981 Β· updates every 60s
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