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Home/Chain Registry/Block #3,153,385

Block #3,153,385

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/24/2019, 11:52:29 AM Β· Difficulty 11.3235 Β· 3,685,524 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1b30027c94256b0cc4d87c773c78436b55355fc1affbbf16ed814a2cc1644119
View on Chainz β†—

Difficulty

11.323523

Transactions

1

Size

201 B

Version

2

Bits

0b52d264

Nonce

405,393,066

Timestamp

4/24/2019, 11:52:29 AM

Confirmations

3,685,524

Merkle Root

e6c21d25773ea69f7738d0232f3534decaba480614a2681a08fb16d52ba045f5
Transactions (1)
Coinbasee6c21d25773ea6…fb16d52ba045f5
1 in β†’ 1 out7.7900 XPM110 B
AbXwmGxD…4XXYP765
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.

1.803 Γ— 10⁹⁷(98-digit number)
18031695487309222257…97151553196695221760
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
1.803 Γ— 10⁹⁷(98-digit number)
18031695487309222257…97151553196695221761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.606 Γ— 10⁹⁷(98-digit number)
36063390974618444514…94303106393390443521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.212 Γ— 10⁹⁷(98-digit number)
72126781949236889028…88606212786780887041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.442 Γ— 10⁹⁸(99-digit number)
14425356389847377805…77212425573561774081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.885 Γ— 10⁹⁸(99-digit number)
28850712779694755611…54424851147123548161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.770 Γ— 10⁹⁸(99-digit number)
57701425559389511222…08849702294247096321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.154 Γ— 10⁹⁹(100-digit number)
11540285111877902244…17699404588494192641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.308 Γ— 10⁹⁹(100-digit number)
23080570223755804489…35398809176988385281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.616 Γ— 10⁹⁹(100-digit number)
46161140447511608978…70797618353976770561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.232 Γ— 10⁹⁹(100-digit number)
92322280895023217956…41595236707953541121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.846 Γ— 10¹⁰⁰(101-digit number)
18464456179004643591…83190473415907082241
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 3153385

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 1b30027c94256b0cc4d87c773c78436b55355fc1affbbf16ed814a2cc1644119

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 #3,153,385 on Chainz β†—
Circulating Supply:57,955,531 XPMΒ·at block #6,838,908 Β· updates every 60s
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