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Home/Chain Registry/Block #2,207,420

Block #2,207,420

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2017, 5:50:54 AM Β· Difficulty 10.9454 Β· 4,632,333 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
50d57fc2c4b1d4fd4807e633267528c205e3062234046d9631add2fd9cac8067
View on Chainz β†—

Difficulty

10.945409

Transactions

2

Size

425 B

Version

2

Bits

0af2064b

Nonce

1,370,098,459

Timestamp

7/15/2017, 5:50:54 AM

Confirmations

4,632,333

Merkle Root

1b7b90e58ba99765e0e08eaf32bde0805eb1a58e3f569b7a4709eea40b599833
Transactions (2)
Coinbasee397c5401746dc…afba062dec63bd
1 in β†’ 1 out8.3400 XPM110 B
AGj3ey1H…iwpGcyVP
f44993e32130bb…5ccfaae98b476c
1 in β†’ 2 out30606.4935 XPM225 B
AMNqyy2W…ise9w8w1AQJN27UR…WSzUpUtR
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.

1.290 Γ— 10⁹⁴(95-digit number)
12903953346205136157…33437642744873578240
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
1.290 Γ— 10⁹⁴(95-digit number)
12903953346205136157…33437642744873578241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.580 Γ— 10⁹⁴(95-digit number)
25807906692410272315…66875285489747156481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.161 Γ— 10⁹⁴(95-digit number)
51615813384820544631…33750570979494312961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.032 Γ— 10⁹⁡(96-digit number)
10323162676964108926…67501141958988625921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.064 Γ— 10⁹⁡(96-digit number)
20646325353928217852…35002283917977251841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.129 Γ— 10⁹⁡(96-digit number)
41292650707856435705…70004567835954503681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.258 Γ— 10⁹⁡(96-digit number)
82585301415712871410…40009135671909007361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.651 Γ— 10⁹⁢(97-digit number)
16517060283142574282…80018271343818014721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.303 Γ— 10⁹⁢(97-digit number)
33034120566285148564…60036542687636029441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.606 Γ— 10⁹⁢(97-digit number)
66068241132570297128…20073085375272058881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.321 Γ— 10⁹⁷(98-digit number)
13213648226514059425…40146170750544117761
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 2207420

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 50d57fc2c4b1d4fd4807e633267528c205e3062234046d9631add2fd9cac8067

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 #2,207,420 on Chainz β†—
Circulating Supply:57,962,311 XPMΒ·at block #6,839,752 Β· updates every 60s
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