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Home/Chain Registry/Block #2,641,729

Block #2,641,729

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2018, 11:27:58 AM Β· Difficulty 11.6294 Β· 4,190,107 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a01674a543cb5aad7c76ba8a8165de8862af5c02f567c129392b297684f28e0b
View on Chainz β†—

Difficulty

11.629379

Transactions

2

Size

427 B

Version

2

Bits

0ba11efa

Nonce

1,366,724,321

Timestamp

5/1/2018, 11:27:58 AM

Confirmations

4,190,107

Merkle Root

02f7732a93afb8cd5f6076e4b9b7696dcc0c48abe025218b0b7938ca11a0a33a
Transactions (2)
Coinbaseac24a0a4196107…6d5e4c70238de9
1 in β†’ 1 out7.3900 XPM110 B
Ac8UCzQ3…4LhiYa6v
0b3480b95fe4b4…f60b7c5c85ca75
1 in β†’ 2 out3456.1568 XPM226 B
AcizX6kn…rSuFPRtgAdCA6h2j…wQX1wymn
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.

2.967 Γ— 10⁹⁢(97-digit number)
29678407525148479470…18892083857981390720
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
2.967 Γ— 10⁹⁢(97-digit number)
29678407525148479470…18892083857981390719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.935 Γ— 10⁹⁢(97-digit number)
59356815050296958941…37784167715962781439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.187 Γ— 10⁹⁷(98-digit number)
11871363010059391788…75568335431925562879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.374 Γ— 10⁹⁷(98-digit number)
23742726020118783576…51136670863851125759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.748 Γ— 10⁹⁷(98-digit number)
47485452040237567153…02273341727702251519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.497 Γ— 10⁹⁷(98-digit number)
94970904080475134306…04546683455404503039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.899 Γ— 10⁹⁸(99-digit number)
18994180816095026861…09093366910809006079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.798 Γ— 10⁹⁸(99-digit number)
37988361632190053722…18186733821618012159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.597 Γ— 10⁹⁸(99-digit number)
75976723264380107445…36373467643236024319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.519 Γ— 10⁹⁹(100-digit number)
15195344652876021489…72746935286472048639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.039 Γ— 10⁹⁹(100-digit number)
30390689305752042978…45493870572944097279
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 2641729

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 a01674a543cb5aad7c76ba8a8165de8862af5c02f567c129392b297684f28e0b

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 #2,641,729 on Chainz β†—
Circulating Supply:57,898,808 XPMΒ·at block #6,831,835 Β· updates every 60s
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