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Home/Chain Registry/Block #3,140,561

Block #3,140,561

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/15/2019, 3:18:57 PM Β· Difficulty 11.3134 Β· 3,692,226 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
27ed73a1fed2d6c06ce210691035129a59d4092d2ab78a7b44a972ea27974e26
View on Chainz β†—

Difficulty

11.313400

Transactions

1

Size

200 B

Version

2

Bits

0b503afb

Nonce

728,128,498

Timestamp

4/15/2019, 3:18:57 PM

Confirmations

3,692,226

Merkle Root

ff3f5d2f3d401defa80a1586e132021562e72c4a0023b1d314dde0202db9bd23
Transactions (1)
Coinbaseff3f5d2f3d401d…dde0202db9bd23
1 in β†’ 1 out7.8000 XPM110 B
AbXwmGxD…4XXYP765
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.

4.460 Γ— 10⁹⁡(96-digit number)
44605133192056938664…96834814489282560160
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
4.460 Γ— 10⁹⁡(96-digit number)
44605133192056938664…96834814489282560159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.921 Γ— 10⁹⁡(96-digit number)
89210266384113877329…93669628978565120319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.784 Γ— 10⁹⁢(97-digit number)
17842053276822775465…87339257957130240639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.568 Γ— 10⁹⁢(97-digit number)
35684106553645550931…74678515914260481279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.136 Γ— 10⁹⁢(97-digit number)
71368213107291101863…49357031828520962559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.427 Γ— 10⁹⁷(98-digit number)
14273642621458220372…98714063657041925119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.854 Γ— 10⁹⁷(98-digit number)
28547285242916440745…97428127314083850239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.709 Γ— 10⁹⁷(98-digit number)
57094570485832881490…94856254628167700479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.141 Γ— 10⁹⁸(99-digit number)
11418914097166576298…89712509256335400959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.283 Γ— 10⁹⁸(99-digit number)
22837828194333152596…79425018512670801919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.567 Γ— 10⁹⁸(99-digit number)
45675656388666305192…58850037025341603839
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 3140561

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 27ed73a1fed2d6c06ce210691035129a59d4092d2ab78a7b44a972ea27974e26

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 #3,140,561 on Chainz β†—
Circulating Supply:57,906,463 XPMΒ·at block #6,832,786 Β· updates every 60s
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