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Block #281,177

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/28/2013, 10:36:05 PM Β· Difficulty 9.9764 Β· 6,519,644 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3bfc54c62721d121df8046d7f95a3ff4931e0961df9755103e71abd216a1da99
View on Chainz β†—

Height

#281,177

Difficulty

9.976409

Transactions

1

Size

187 B

Version

2

Bits

09f9f5f3

Nonce

171,996

Timestamp

11/28/2013, 10:36:05 PM

Confirmations

6,519,644

Merkle Root

e8a1c17421d1f53f04fc7132f82e208bb6ab75ae1596379281761b7bedf8e21a
Transactions (1)
Coinbasee8a1c17421d1f5…761b7bedf8e21a
1 in β†’ 1 out10.0300 XPM97 B
AWQBKr3Y…sUA1Ehpd
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.

4.653 Γ— 10⁹⁡(96-digit number)
46532457457847174253…62621262506184724480
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
4.653 Γ— 10⁹⁡(96-digit number)
46532457457847174253…62621262506184724479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.306 Γ— 10⁹⁡(96-digit number)
93064914915694348506…25242525012369448959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.861 Γ— 10⁹⁢(97-digit number)
18612982983138869701…50485050024738897919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.722 Γ— 10⁹⁢(97-digit number)
37225965966277739402…00970100049477795839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.445 Γ— 10⁹⁢(97-digit number)
74451931932555478805…01940200098955591679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.489 Γ— 10⁹⁷(98-digit number)
14890386386511095761…03880400197911183359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.978 Γ— 10⁹⁷(98-digit number)
29780772773022191522…07760800395822366719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.956 Γ— 10⁹⁷(98-digit number)
59561545546044383044…15521600791644733439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.191 Γ— 10⁹⁸(99-digit number)
11912309109208876608…31043201583289466879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.382 Γ— 10⁹⁸(99-digit number)
23824618218417753217…62086403166578933759
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 281177

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 3bfc54c62721d121df8046d7f95a3ff4931e0961df9755103e71abd216a1da99

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 #281,177 on Chainz β†—
Circulating Supply:57,650,624 XPMΒ·at block #6,800,820 Β· updates every 60s
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