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Home/Chain Registry/Block #3,155,364

Block #3,155,364

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/25/2019, 9:19:28 PM Β· Difficulty 11.3199 Β· 3,685,429 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4a3936fbe1c403c3ead4b9f2e3b3cf4547953001fe3c8aeeff32e430a4041e60
View on Chainz β†—

Difficulty

11.319945

Transactions

1

Size

200 B

Version

2

Bits

0b51e7f0

Nonce

130,953,518

Timestamp

4/25/2019, 9:19:28 PM

Confirmations

3,685,429

Merkle Root

1ede7aac869c5a409f82910d502ae6a849b2e53fc0035ae0aa79250e8aae8859
Transactions (1)
Coinbase1ede7aac869c5a…79250e8aae8859
1 in β†’ 1 out7.7900 XPM110 B
AUMQRepm…tAfKmdW1
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.

4.669 Γ— 10⁹⁡(96-digit number)
46693838547074300338…55493736587890556160
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
4.669 Γ— 10⁹⁡(96-digit number)
46693838547074300338…55493736587890556159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.338 Γ— 10⁹⁡(96-digit number)
93387677094148600676…10987473175781112319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.867 Γ— 10⁹⁢(97-digit number)
18677535418829720135…21974946351562224639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.735 Γ— 10⁹⁢(97-digit number)
37355070837659440270…43949892703124449279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.471 Γ— 10⁹⁢(97-digit number)
74710141675318880541…87899785406248898559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.494 Γ— 10⁹⁷(98-digit number)
14942028335063776108…75799570812497797119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.988 Γ— 10⁹⁷(98-digit number)
29884056670127552216…51599141624995594239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.976 Γ— 10⁹⁷(98-digit number)
59768113340255104433…03198283249991188479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.195 Γ— 10⁹⁸(99-digit number)
11953622668051020886…06396566499982376959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.390 Γ— 10⁹⁸(99-digit number)
23907245336102041773…12793132999964753919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.781 Γ— 10⁹⁸(99-digit number)
47814490672204083546…25586265999929507839
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 3155364

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 4a3936fbe1c403c3ead4b9f2e3b3cf4547953001fe3c8aeeff32e430a4041e60

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 #3,155,364 on Chainz β†—
Circulating Supply:57,970,691 XPMΒ·at block #6,840,792 Β· updates every 60s
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