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Home/Chain Registry/Block #3,197,319

Block #3,197,319

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2019, 3:09:28 PM Β· Difficulty 11.1927 Β· 3,645,722 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ca01b6dd9ec821e5dd6d7e20cd045fe47983a03551bceee3ea2e350fff73704
View on Chainz β†—

Difficulty

11.192726

Transactions

2

Size

7.49 KB

Version

2

Bits

0b31567f

Nonce

1,577,218,659

Timestamp

5/25/2019, 3:09:28 PM

Confirmations

3,645,722

Merkle Root

16b41b526fdfd9bbf4a9cc11a82c2af9a4f631e933cf26a4c9e6360f9d128133
Transactions (2)
Coinbase6ef57ac079e210…9aedd81918f7ab
1 in β†’ 1 out8.0800 XPM109 B
AQkxNuoB…VZPKouPM
9aa815395ccd9b…cecba6c8354600
50 in β†’ 2 out1990.9883 XPM7.30 KB
ANu6LqLe…o9SLEevcAPQ9gg1V…H4v8MyZ4
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.

1.921 Γ— 10⁹⁡(96-digit number)
19214063940923670633…25572785694317776000
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.921 Γ— 10⁹⁡(96-digit number)
19214063940923670633…25572785694317776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.842 Γ— 10⁹⁡(96-digit number)
38428127881847341267…51145571388635552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.685 Γ— 10⁹⁡(96-digit number)
76856255763694682534…02291142777271104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.537 Γ— 10⁹⁢(97-digit number)
15371251152738936506…04582285554542208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.074 Γ— 10⁹⁢(97-digit number)
30742502305477873013…09164571109084416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.148 Γ— 10⁹⁢(97-digit number)
61485004610955746027…18329142218168832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.229 Γ— 10⁹⁷(98-digit number)
12297000922191149205…36658284436337664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.459 Γ— 10⁹⁷(98-digit number)
24594001844382298410…73316568872675328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.918 Γ— 10⁹⁷(98-digit number)
49188003688764596821…46633137745350656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.837 Γ— 10⁹⁷(98-digit number)
98376007377529193643…93266275490701312001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.967 Γ— 10⁹⁸(99-digit number)
19675201475505838728…86532550981402624001
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 3197319

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 6ca01b6dd9ec821e5dd6d7e20cd045fe47983a03551bceee3ea2e350fff73704

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 #3,197,319 on Chainz β†—
Circulating Supply:57,988,685 XPMΒ·at block #6,843,040 Β· updates every 60s
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