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Block #2,953,463

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/5/2018, 6:07:29 PM Β· Difficulty 11.4001 Β· 3,888,407 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
035faa48ee06ca6a6ab7f97c4051b43ab4e797ff3383d4d5b960bf8a92ff8f2c
View on Chainz β†—

Difficulty

11.400057

Transactions

1

Size

200 B

Version

2

Bits

0b666a26

Nonce

1,390,446,176

Timestamp

12/5/2018, 6:07:29 PM

Confirmations

3,888,407

Merkle Root

d07b1ba2d90702c38741850c2688980e31c4e88128fa0dbe7680633fe91d1ac9
Transactions (1)
Coinbased07b1ba2d90702…80633fe91d1ac9
1 in β†’ 1 out7.6800 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.

1.135 Γ— 10⁹⁡(96-digit number)
11352515816321509327…67286059056725751520
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
1.135 Γ— 10⁹⁡(96-digit number)
11352515816321509327…67286059056725751519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.270 Γ— 10⁹⁡(96-digit number)
22705031632643018654…34572118113451503039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.541 Γ— 10⁹⁡(96-digit number)
45410063265286037309…69144236226903006079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.082 Γ— 10⁹⁡(96-digit number)
90820126530572074618…38288472453806012159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.816 Γ— 10⁹⁢(97-digit number)
18164025306114414923…76576944907612024319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.632 Γ— 10⁹⁢(97-digit number)
36328050612228829847…53153889815224048639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.265 Γ— 10⁹⁢(97-digit number)
72656101224457659694…06307779630448097279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.453 Γ— 10⁹⁷(98-digit number)
14531220244891531938…12615559260896194559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.906 Γ— 10⁹⁷(98-digit number)
29062440489783063877…25231118521792389119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.812 Γ— 10⁹⁷(98-digit number)
58124880979566127755…50462237043584778239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.162 Γ— 10⁹⁸(99-digit number)
11624976195913225551…00924474087169556479
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 2953463

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 035faa48ee06ca6a6ab7f97c4051b43ab4e797ff3383d4d5b960bf8a92ff8f2c

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 #2,953,463 on Chainz β†—
Circulating Supply:57,979,337 XPMΒ·at block #6,841,869 Β· updates every 60s
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