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Home/Chain Registry/Block #2,641,919

Block #2,641,919

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2018, 12:59:09 PM Β· Difficulty 11.6366 Β· 4,203,734 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
775ae8410664c0b8558b8605417ae0444e3efe4055f805f653dee0cb9fc82060
View on Chainz β†—

Difficulty

11.636565

Transactions

2

Size

47.54 KB

Version

2

Bits

0ba2f5e6

Nonce

518,478,438

Timestamp

5/1/2018, 12:59:09 PM

Confirmations

4,203,734

Merkle Root

04988cd017ebf65b14c1392fe92ae87e7a4011c92daaa6e351762d638493f503
Transactions (2)
Coinbase453b8051458d65…123803a3c46b2e
1 in β†’ 1 out7.9600 XPM110 B
AeMDc7tC…mZoetidb
0436df765cf469…c1f10241619b47
327 in β†’ 2 out4000.0100 XPM47.35 KB
AUdrfVq1…z6CVgkYuALPF8J52…Hjw4BMsG
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.

5.992 Γ— 10⁹⁡(96-digit number)
59920475855623572465…28244182283407586560
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
5.992 Γ— 10⁹⁡(96-digit number)
59920475855623572465…28244182283407586559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.198 Γ— 10⁹⁢(97-digit number)
11984095171124714493…56488364566815173119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.396 Γ— 10⁹⁢(97-digit number)
23968190342249428986…12976729133630346239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.793 Γ— 10⁹⁢(97-digit number)
47936380684498857972…25953458267260692479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.587 Γ— 10⁹⁢(97-digit number)
95872761368997715945…51906916534521384959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.917 Γ— 10⁹⁷(98-digit number)
19174552273799543189…03813833069042769919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.834 Γ— 10⁹⁷(98-digit number)
38349104547599086378…07627666138085539839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.669 Γ— 10⁹⁷(98-digit number)
76698209095198172756…15255332276171079679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.533 Γ— 10⁹⁸(99-digit number)
15339641819039634551…30510664552342159359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.067 Γ— 10⁹⁸(99-digit number)
30679283638079269102…61021329104684318719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.135 Γ— 10⁹⁸(99-digit number)
61358567276158538205…22042658209368637439
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 2641919

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 775ae8410664c0b8558b8605417ae0444e3efe4055f805f653dee0cb9fc82060

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 #2,641,919 on Chainz β†—
Circulating Supply:58,009,672 XPMΒ·at block #6,845,652 Β· updates every 60s
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