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Home/Chain Registry/Block #1,533,415

Block #1,533,415

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/9/2016, 1:00:58 PM Β· Difficulty 10.6167 Β· 5,281,443 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cfdb872d00b59eccb27d9ae26224bce5cc5582c331bd4f802e62b9bf4d521bc4
View on Chainz β†—

Difficulty

10.616663

Transactions

1

Size

243 B

Version

2

Bits

0a9ddda5

Nonce

1,511,834,941

Timestamp

4/9/2016, 1:00:58 PM

Confirmations

5,281,443

Merkle Root

ba5317b3782926f0f7749f8e2aae19f76eaf88b1a7769e277ca434dd37ef0c95
Transactions (1)
Coinbaseba5317b3782926…a434dd37ef0c95
1 in β†’ 2 out8.8600 XPM152 B
AeNeFst2…6pebBnhdALPu3s2c…EJXLjVFh
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.

6.540 Γ— 10⁹⁷(98-digit number)
65402445759527843738…80363125084528816640
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
6.540 Γ— 10⁹⁷(98-digit number)
65402445759527843738…80363125084528816639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.308 Γ— 10⁹⁸(99-digit number)
13080489151905568747…60726250169057633279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.616 Γ— 10⁹⁸(99-digit number)
26160978303811137495…21452500338115266559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.232 Γ— 10⁹⁸(99-digit number)
52321956607622274990…42905000676230533119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.046 Γ— 10⁹⁹(100-digit number)
10464391321524454998…85810001352461066239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.092 Γ— 10⁹⁹(100-digit number)
20928782643048909996…71620002704922132479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.185 Γ— 10⁹⁹(100-digit number)
41857565286097819992…43240005409844264959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.371 Γ— 10⁹⁹(100-digit number)
83715130572195639985…86480010819688529919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.674 Γ— 10¹⁰⁰(101-digit number)
16743026114439127997…72960021639377059839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.348 Γ— 10¹⁰⁰(101-digit number)
33486052228878255994…45920043278754119679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1533415

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 cfdb872d00b59eccb27d9ae26224bce5cc5582c331bd4f802e62b9bf4d521bc4

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 #1,533,415 on Chainz β†—
Circulating Supply:57,762,948 XPMΒ·at block #6,814,857 Β· updates every 60s
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