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Block #3,506,477

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/9/2020, 8:20:19 AM Β· Difficulty 10.9307 Β· 3,319,000 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9587455cf8190ccde09a7db2279871c3e353b77f8ee536ec1d855d26a13d11f5
View on Chainz β†—

Difficulty

10.930656

Transactions

1

Size

199 B

Version

2

Bits

0aee3f75

Nonce

2,148,648,176

Timestamp

1/9/2020, 8:20:19 AM

Confirmations

3,319,000

Merkle Root

5ea0f5a5ed4c3880455b4f9bd7c0d0819f51bc69ac48e4be72de3b359924b0f2
Transactions (1)
Coinbase5ea0f5a5ed4c38…de3b359924b0f2
1 in β†’ 1 out8.3600 XPM109 B
ASiq2qtK…VMhmk7yL
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.

5.074 Γ— 10⁹⁡(96-digit number)
50747924363505281821…92177111127436185600
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
5.074 Γ— 10⁹⁡(96-digit number)
50747924363505281821…92177111127436185599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.014 Γ— 10⁹⁢(97-digit number)
10149584872701056364…84354222254872371199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.029 Γ— 10⁹⁢(97-digit number)
20299169745402112728…68708444509744742399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.059 Γ— 10⁹⁢(97-digit number)
40598339490804225457…37416889019489484799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.119 Γ— 10⁹⁢(97-digit number)
81196678981608450914…74833778038978969599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.623 Γ— 10⁹⁷(98-digit number)
16239335796321690182…49667556077957939199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.247 Γ— 10⁹⁷(98-digit number)
32478671592643380365…99335112155915878399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.495 Γ— 10⁹⁷(98-digit number)
64957343185286760731…98670224311831756799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.299 Γ— 10⁹⁸(99-digit number)
12991468637057352146…97340448623663513599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.598 Γ— 10⁹⁸(99-digit number)
25982937274114704292…94680897247327027199
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 3506477

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 9587455cf8190ccde09a7db2279871c3e353b77f8ee536ec1d855d26a13d11f5

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 #3,506,477 on Chainz β†—
Circulating Supply:57,847,910 XPMΒ·at block #6,825,476 Β· updates every 60s
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