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Home/Chain Registry/Block #2,872,623

Block #2,872,623

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/8/2018, 1:00:17 PM Β· Difficulty 11.6661 Β· 3,961,298 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bb086b72bb61c3f7a9c244779a97848f81b5da3f196415f69a7fa16c45718a8c
View on Chainz β†—

Difficulty

11.666086

Transactions

1

Size

200 B

Version

2

Bits

0baa8497

Nonce

1,306,258,997

Timestamp

10/8/2018, 1:00:17 PM

Confirmations

3,961,298

Merkle Root

1453174b36a94150ded47b34d436337b0d110fb5077d2bb78215acaaaf98db67
Transactions (1)
Coinbase1453174b36a941…15acaaaf98db67
1 in β†’ 1 out7.3400 XPM110 B
AUJxgs6p…k84p2Fhp
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.

5.725 Γ— 10⁹⁴(95-digit number)
57257944347517520468…45454662677873852480
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
5.725 Γ— 10⁹⁴(95-digit number)
57257944347517520468…45454662677873852479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.145 Γ— 10⁹⁡(96-digit number)
11451588869503504093…90909325355747704959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.290 Γ— 10⁹⁡(96-digit number)
22903177739007008187…81818650711495409919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.580 Γ— 10⁹⁡(96-digit number)
45806355478014016375…63637301422990819839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.161 Γ— 10⁹⁡(96-digit number)
91612710956028032750…27274602845981639679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.832 Γ— 10⁹⁢(97-digit number)
18322542191205606550…54549205691963279359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.664 Γ— 10⁹⁢(97-digit number)
36645084382411213100…09098411383926558719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.329 Γ— 10⁹⁢(97-digit number)
73290168764822426200…18196822767853117439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.465 Γ— 10⁹⁷(98-digit number)
14658033752964485240…36393645535706234879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.931 Γ— 10⁹⁷(98-digit number)
29316067505928970480…72787291071412469759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.863 Γ— 10⁹⁷(98-digit number)
58632135011857940960…45574582142824939519
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 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
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 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 2872623

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 bb086b72bb61c3f7a9c244779a97848f81b5da3f196415f69a7fa16c45718a8c

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 #2,872,623 on Chainz β†—
Circulating Supply:57,915,595 XPMΒ·at block #6,833,920 Β· updates every 60s
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