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Home/Chain Registry/Block #2,172,999

Block #2,172,999

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/23/2017, 1:04:19 AM Β· Difficulty 10.9095 Β· 4,659,627 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e8b90f6801d9b2b4f4749bcf07dbd128d9ad8276ea2ccb380041b9feebb33760
View on Chainz β†—

Difficulty

10.909469

Transactions

1

Size

200 B

Version

2

Bits

0ae8d2f0

Nonce

557,465,408

Timestamp

6/23/2017, 1:04:19 AM

Confirmations

4,659,627

Merkle Root

9f86b1ef58a415df0cd079dd5edb54a42e2eacf4bc8352db761e1ffbeddfce03
Transactions (1)
Coinbase9f86b1ef58a415…1e1ffbeddfce03
1 in β†’ 1 out8.3900 XPM110 B
AQomBXwb…sRhxrbk1
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.

7.078 Γ— 10⁹⁴(95-digit number)
70782620966860482608…82988426301281110640
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
7.078 Γ— 10⁹⁴(95-digit number)
70782620966860482608…82988426301281110639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.415 Γ— 10⁹⁡(96-digit number)
14156524193372096521…65976852602562221279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.831 Γ— 10⁹⁡(96-digit number)
28313048386744193043…31953705205124442559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.662 Γ— 10⁹⁡(96-digit number)
56626096773488386087…63907410410248885119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.132 Γ— 10⁹⁢(97-digit number)
11325219354697677217…27814820820497770239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.265 Γ— 10⁹⁢(97-digit number)
22650438709395354434…55629641640995540479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.530 Γ— 10⁹⁢(97-digit number)
45300877418790708869…11259283281991080959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.060 Γ— 10⁹⁢(97-digit number)
90601754837581417739…22518566563982161919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.812 Γ— 10⁹⁷(98-digit number)
18120350967516283547…45037133127964323839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.624 Γ— 10⁹⁷(98-digit number)
36240701935032567095…90074266255928647679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First 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
UncommonChain length 10
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2172999

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 e8b90f6801d9b2b4f4749bcf07dbd128d9ad8276ea2ccb380041b9feebb33760

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 #2,172,999 on Chainz β†—
Circulating Supply:57,905,156 XPMΒ·at block #6,832,625 Β· updates every 60s
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