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Block #3,085,615

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/9/2019, 4:27:20 PM Β· Difficulty 11.0287 Β· 3,756,727 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
65ced48fb583b8efb83141b4fb91cac3bd8ee5ce10fe7b8f0e48d9c5cd903030
View on Chainz β†—

Difficulty

11.028718

Transactions

1

Size

200 B

Version

2

Bits

0b075a15

Nonce

479,918,837

Timestamp

3/9/2019, 4:27:20 PM

Confirmations

3,756,727

Merkle Root

5e0ab8efb306d0fd02eb2136fc37215edf8fb9878021a773580ac256ee00d090
Transactions (1)
Coinbase5e0ab8efb306d0…0ac256ee00d090
1 in β†’ 1 out8.2100 XPM110 B
AUhjokok…k5m93PZR
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.

1.229 Γ— 10⁹⁡(96-digit number)
12291926945289875507…16205546797056111210
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
1.229 Γ— 10⁹⁡(96-digit number)
12291926945289875507…16205546797056111209
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.458 Γ— 10⁹⁡(96-digit number)
24583853890579751015…32411093594112222419
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.916 Γ— 10⁹⁡(96-digit number)
49167707781159502030…64822187188224444839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.833 Γ— 10⁹⁡(96-digit number)
98335415562319004061…29644374376448889679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.966 Γ— 10⁹⁢(97-digit number)
19667083112463800812…59288748752897779359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.933 Γ— 10⁹⁢(97-digit number)
39334166224927601624…18577497505795558719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.866 Γ— 10⁹⁢(97-digit number)
78668332449855203248…37154995011591117439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.573 Γ— 10⁹⁷(98-digit number)
15733666489971040649…74309990023182234879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.146 Γ— 10⁹⁷(98-digit number)
31467332979942081299…48619980046364469759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.293 Γ— 10⁹⁷(98-digit number)
62934665959884162599…97239960092728939519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.258 Γ— 10⁹⁸(99-digit number)
12586933191976832519…94479920185457879039
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 3085615

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 65ced48fb583b8efb83141b4fb91cac3bd8ee5ce10fe7b8f0e48d9c5cd903030

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 #3,085,615 on Chainz β†—
Circulating Supply:57,983,142 XPMΒ·at block #6,842,341 Β· updates every 60s
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