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Home/Chain Registry/Block #2,267,315

Block #2,267,315

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/25/2017, 12:42:32 PM Β· Difficulty 10.9517 Β· 4,566,649 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
79afd12332403675626553bd5d7167139a0534d23ee8cf9c1ad54e834540cad7
View on Chainz β†—

Difficulty

10.951703

Transactions

1

Size

201 B

Version

2

Bits

0af3a2c7

Nonce

293,096,895

Timestamp

8/25/2017, 12:42:32 PM

Confirmations

4,566,649

Merkle Root

b0b1bafd90a7c7f508b0f6cf44e83a4f0e48efbe923e0021d9b7a8bf4575d8c3
Transactions (1)
Coinbaseb0b1bafd90a7c7…b7a8bf4575d8c3
1 in β†’ 1 out8.3200 XPM110 B
AP9jv7ri…vVXQLXFW
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.

4.800 Γ— 10⁹⁢(97-digit number)
48006428988987017260…89671423853437711360
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
4.800 Γ— 10⁹⁢(97-digit number)
48006428988987017260…89671423853437711359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.601 Γ— 10⁹⁢(97-digit number)
96012857977974034520…79342847706875422719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.920 Γ— 10⁹⁷(98-digit number)
19202571595594806904…58685695413750845439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.840 Γ— 10⁹⁷(98-digit number)
38405143191189613808…17371390827501690879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.681 Γ— 10⁹⁷(98-digit number)
76810286382379227616…34742781655003381759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.536 Γ— 10⁹⁸(99-digit number)
15362057276475845523…69485563310006763519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.072 Γ— 10⁹⁸(99-digit number)
30724114552951691046…38971126620013527039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.144 Γ— 10⁹⁸(99-digit number)
61448229105903382093…77942253240027054079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.228 Γ— 10⁹⁹(100-digit number)
12289645821180676418…55884506480054108159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.457 Γ— 10⁹⁹(100-digit number)
24579291642361352837…11769012960108216319
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 2267315

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 79afd12332403675626553bd5d7167139a0534d23ee8cf9c1ad54e834540cad7

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 #2,267,315 on Chainz β†—
Circulating Supply:57,915,941 XPMΒ·at block #6,833,963 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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