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Home/Chain Registry/Block #3,445,443

Block #3,445,443

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/23/2019, 1:11:56 PM Β· Difficulty 10.9789 Β· 3,368,467 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1c500430821bc3bde97121d707e73d128b22e0fba7a76cb6ce3dbfe8a45801dd
View on Chainz β†—

Difficulty

10.978895

Transactions

1

Size

200 B

Version

2

Bits

0afa98d8

Nonce

2,038,755,463

Timestamp

11/23/2019, 1:11:56 PM

Confirmations

3,368,467

Merkle Root

11ebfc6796d053578596e38f728f684f55d39b5ad637574843e620e647a037f4
Transactions (1)
Coinbase11ebfc6796d053…e620e647a037f4
1 in β†’ 1 out8.2800 XPM109 B
ARvZEYK7…bZ6zRpvK
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.

1.969 Γ— 10⁹⁷(98-digit number)
19693013521233631526…66605186435160064000
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
1.969 Γ— 10⁹⁷(98-digit number)
19693013521233631526…66605186435160063999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.938 Γ— 10⁹⁷(98-digit number)
39386027042467263052…33210372870320127999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.877 Γ— 10⁹⁷(98-digit number)
78772054084934526104…66420745740640255999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.575 Γ— 10⁹⁸(99-digit number)
15754410816986905220…32841491481280511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.150 Γ— 10⁹⁸(99-digit number)
31508821633973810441…65682982962561023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.301 Γ— 10⁹⁸(99-digit number)
63017643267947620883…31365965925122047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.260 Γ— 10⁹⁹(100-digit number)
12603528653589524176…62731931850244095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.520 Γ— 10⁹⁹(100-digit number)
25207057307179048353…25463863700488191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.041 Γ— 10⁹⁹(100-digit number)
50414114614358096707…50927727400976383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.008 Γ— 10¹⁰⁰(101-digit number)
10082822922871619341…01855454801952767999
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 3445443

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 1c500430821bc3bde97121d707e73d128b22e0fba7a76cb6ce3dbfe8a45801dd

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 #3,445,443 on Chainz β†—
Circulating Supply:57,755,352 XPMΒ·at block #6,813,909 Β· updates every 60s
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