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Home/Chain Registry/Block #2,237,071

Block #2,237,071

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/4/2017, 7:59:07 PM Β· Difficulty 10.9463 Β· 4,605,921 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a7fc9939b3b951e9204cf3c1e4090cbf1bfc498b7428bc67578b64ca4a2a5091
View on Chainz β†—

Difficulty

10.946334

Transactions

1

Size

200 B

Version

2

Bits

0af242f0

Nonce

832,636,446

Timestamp

8/4/2017, 7:59:07 PM

Confirmations

4,605,921

Merkle Root

acb6d85088e3e9130180c4c85728762ad29f5f459876d26082bd90e91039f71d
Transactions (1)
Coinbaseacb6d85088e3e9…bd90e91039f71d
1 in β†’ 1 out8.3300 XPM110 B
AcWMDcVu…LNcfr5o1
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.

6.525 Γ— 10⁹⁴(95-digit number)
65257562772614836558…19169155607099575680
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
6.525 Γ— 10⁹⁴(95-digit number)
65257562772614836558…19169155607099575681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.305 Γ— 10⁹⁡(96-digit number)
13051512554522967311…38338311214199151361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.610 Γ— 10⁹⁡(96-digit number)
26103025109045934623…76676622428398302721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.220 Γ— 10⁹⁡(96-digit number)
52206050218091869247…53353244856796605441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.044 Γ— 10⁹⁢(97-digit number)
10441210043618373849…06706489713593210881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.088 Γ— 10⁹⁢(97-digit number)
20882420087236747698…13412979427186421761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.176 Γ— 10⁹⁢(97-digit number)
41764840174473495397…26825958854372843521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.352 Γ— 10⁹⁢(97-digit number)
83529680348946990795…53651917708745687041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.670 Γ— 10⁹⁷(98-digit number)
16705936069789398159…07303835417491374081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.341 Γ— 10⁹⁷(98-digit number)
33411872139578796318…14607670834982748161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.682 Γ— 10⁹⁷(98-digit number)
66823744279157592636…29215341669965496321
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 2237071

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 a7fc9939b3b951e9204cf3c1e4090cbf1bfc498b7428bc67578b64ca4a2a5091

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 #2,237,071 on Chainz β†—
Circulating Supply:57,988,292 XPMΒ·at block #6,842,991 Β· updates every 60s
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