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Home/Chain Registry/Block #2,914,197

Block #2,914,197

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/7/2018, 11:33:41 PM Β· Difficulty 11.4793 Β· 3,917,828 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f33bcddb3346ea2097114f1dad621bc0d775f72be4e74227406f2e9b287d8694
View on Chainz β†—

Difficulty

11.479338

Transactions

1

Size

199 B

Version

2

Bits

0b7ab5eb

Nonce

1,184,030,611

Timestamp

11/7/2018, 11:33:41 PM

Confirmations

3,917,828

Merkle Root

deb7a9694adde7f7a7ccfaa4f2bb812107b2e7db3b643eb327c328f1dafa89fb
Transactions (1)
Coinbasedeb7a9694adde7…c328f1dafa89fb
1 in β†’ 1 out7.5800 XPM109 B
AXqcNr41…xWmnvPpG
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.

9.060 Γ— 10⁹⁴(95-digit number)
90607401173164802431…28776745909516646400
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
9.060 Γ— 10⁹⁴(95-digit number)
90607401173164802431…28776745909516646399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.812 Γ— 10⁹⁡(96-digit number)
18121480234632960486…57553491819033292799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.624 Γ— 10⁹⁡(96-digit number)
36242960469265920972…15106983638066585599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.248 Γ— 10⁹⁡(96-digit number)
72485920938531841945…30213967276133171199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.449 Γ— 10⁹⁢(97-digit number)
14497184187706368389…60427934552266342399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.899 Γ— 10⁹⁢(97-digit number)
28994368375412736778…20855869104532684799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.798 Γ— 10⁹⁢(97-digit number)
57988736750825473556…41711738209065369599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.159 Γ— 10⁹⁷(98-digit number)
11597747350165094711…83423476418130739199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.319 Γ— 10⁹⁷(98-digit number)
23195494700330189422…66846952836261478399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.639 Γ— 10⁹⁷(98-digit number)
46390989400660378844…33693905672522956799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.278 Γ— 10⁹⁷(98-digit number)
92781978801320757689…67387811345045913599
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 2914197

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 f33bcddb3346ea2097114f1dad621bc0d775f72be4e74227406f2e9b287d8694

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 #2,914,197 on Chainz β†—
Circulating Supply:57,900,331 XPMΒ·at block #6,832,024 Β· updates every 60s
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