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Home/Chain Registry/Block #2,913,670

Block #2,913,670

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/7/2018, 1:03:22 PM Β· Difficulty 11.4898 Β· 3,931,387 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f03e91b965e1340da9aa1cf52ac6940653dd62557fec9db3e3ea104834ec5c98
View on Chainz β†—

Difficulty

11.489787

Transactions

1

Size

200 B

Version

2

Bits

0b7d62aa

Nonce

2,145,064,224

Timestamp

11/7/2018, 1:03:22 PM

Confirmations

3,931,387

Merkle Root

e338d7735a277b40190301568006219b7fd1820798fbfc4cca5aa89952a7c5cc
Transactions (1)
Coinbasee338d7735a277b…5aa89952a7c5cc
1 in β†’ 1 out7.5600 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.

4.462 Γ— 10⁹⁡(96-digit number)
44623255982108252988…69932172693694005400
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
4.462 Γ— 10⁹⁡(96-digit number)
44623255982108252988…69932172693694005399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.924 Γ— 10⁹⁡(96-digit number)
89246511964216505977…39864345387388010799
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)
17849302392843301195…79728690774776021599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.569 Γ— 10⁹⁢(97-digit number)
35698604785686602391…59457381549552043199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.139 Γ— 10⁹⁢(97-digit number)
71397209571373204782…18914763099104086399
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)
14279441914274640956…37829526198208172799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.855 Γ— 10⁹⁷(98-digit number)
28558883828549281912…75659052396416345599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.711 Γ— 10⁹⁷(98-digit number)
57117767657098563825…51318104792832691199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.142 Γ— 10⁹⁸(99-digit number)
11423553531419712765…02636209585665382399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.284 Γ— 10⁹⁸(99-digit number)
22847107062839425530…05272419171330764799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.569 Γ— 10⁹⁸(99-digit number)
45694214125678851060…10544838342661529599
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 2913670

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 f03e91b965e1340da9aa1cf52ac6940653dd62557fec9db3e3ea104834ec5c98

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 #2,913,670 on Chainz β†—
Circulating Supply:58,004,880 XPMΒ·at block #6,845,056 Β· updates every 60s
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