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Home/Chain Registry/Block #3,550,108

Block #3,550,108

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/8/2020, 5:20:12 PM Β· Difficulty 10.9306 Β· 3,274,881 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2c62c2ae11f206ab0a269d6498ff3f5265b20c88d964af7c22ccffa7183ab366
View on Chainz β†—

Difficulty

10.930572

Transactions

1

Size

200 B

Version

2

Bits

0aee39fe

Nonce

754,311,685

Timestamp

2/8/2020, 5:20:12 PM

Confirmations

3,274,881

Merkle Root

eaef69b769064681152d244467c9a3fbf1dbca502bf37e4b77e393674c1ca7fd
Transactions (1)
Coinbaseeaef69b7690646…e393674c1ca7fd
1 in β†’ 1 out8.3600 XPM110 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.

4.197 Γ— 10⁹⁡(96-digit number)
41979316118254151793…53862779089646067680
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
4.197 Γ— 10⁹⁡(96-digit number)
41979316118254151793…53862779089646067679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.395 Γ— 10⁹⁡(96-digit number)
83958632236508303586…07725558179292135359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.679 Γ— 10⁹⁢(97-digit number)
16791726447301660717…15451116358584270719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.358 Γ— 10⁹⁢(97-digit number)
33583452894603321434…30902232717168541439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.716 Γ— 10⁹⁢(97-digit number)
67166905789206642869…61804465434337082879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.343 Γ— 10⁹⁷(98-digit number)
13433381157841328573…23608930868674165759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.686 Γ— 10⁹⁷(98-digit number)
26866762315682657147…47217861737348331519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.373 Γ— 10⁹⁷(98-digit number)
53733524631365314295…94435723474696663039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.074 Γ— 10⁹⁸(99-digit number)
10746704926273062859…88871446949393326079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.149 Γ— 10⁹⁸(99-digit number)
21493409852546125718…77742893898786652159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.298 Γ— 10⁹⁸(99-digit number)
42986819705092251436…55485787797573304319
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 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
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 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 3550108

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 2c62c2ae11f206ab0a269d6498ff3f5265b20c88d964af7c22ccffa7183ab366

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 #3,550,108 on Chainz β†—
Circulating Supply:57,843,995 XPMΒ·at block #6,824,988 Β· updates every 60s
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