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Home/Chain Registry/Block #3,244,953

Block #3,244,953

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/28/2019, 4:59:26 PM Β· Difficulty 11.0126 Β· 3,600,162 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
77f7981f04bcc4f9c0ddfd0232300c237e0c2520c88600a851dcb66a01ddce8d
View on Chainz β†—

Difficulty

11.012642

Transactions

1

Size

199 B

Version

2

Bits

0b033c7b

Nonce

211,247,736

Timestamp

6/28/2019, 4:59:26 PM

Confirmations

3,600,162

Merkle Root

9b52698219103f30bce87ca582d92c0990712da7a0e9f6e55be9ddbc6847dd12
Transactions (1)
Coinbase9b52698219103f…e9ddbc6847dd12
1 in β†’ 1 out8.2300 XPM109 B
Aa32y8PQ…e3Enbehj
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.

8.451 Γ— 10⁹⁴(95-digit number)
84513761598471816549…18643854174395106160
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
8.451 Γ— 10⁹⁴(95-digit number)
84513761598471816549…18643854174395106159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.690 Γ— 10⁹⁡(96-digit number)
16902752319694363309…37287708348790212319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.380 Γ— 10⁹⁡(96-digit number)
33805504639388726619…74575416697580424639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.761 Γ— 10⁹⁡(96-digit number)
67611009278777453239…49150833395160849279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.352 Γ— 10⁹⁢(97-digit number)
13522201855755490647…98301666790321698559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.704 Γ— 10⁹⁢(97-digit number)
27044403711510981295…96603333580643397119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.408 Γ— 10⁹⁢(97-digit number)
54088807423021962591…93206667161286794239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.081 Γ— 10⁹⁷(98-digit number)
10817761484604392518…86413334322573588479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.163 Γ— 10⁹⁷(98-digit number)
21635522969208785036…72826668645147176959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.327 Γ— 10⁹⁷(98-digit number)
43271045938417570073…45653337290294353919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.654 Γ— 10⁹⁷(98-digit number)
86542091876835140146…91306674580588707839
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 3244953

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 77f7981f04bcc4f9c0ddfd0232300c237e0c2520c88600a851dcb66a01ddce8d

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 #3,244,953 on Chainz β†—
Circulating Supply:58,005,347 XPMΒ·at block #6,845,114 Β· updates every 60s
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