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Block #275,178

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/26/2013, 2:23:22 PM Β· Difficulty 9.9600 Β· 6,536,896 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
87fa6b64e3c4198b094a4eb6589c4712c3d8be0eadf68bcba5b0decbad8f380d
View on Chainz β†—

Height

#275,178

Difficulty

9.959989

Transactions

1

Size

1.11 KB

Version

2

Bits

09f5c1d8

Nonce

206,259

Timestamp

11/26/2013, 2:23:22 PM

Confirmations

6,536,896

Merkle Root

70d269a1df9f150a9266fb2f03b2b4bc0a6ad198c87b83b865a1f94258938e6d
Transactions (1)
Coinbase70d269a1df9f15…a1f94258938e6d
1 in β†’ 29 out10.0500 XPM1.02 KB
APeshfYV…3PKcKMKHAbv8pzf1…t4zPXDTVAWJZi4km…21vRLENDASdxa9g1…s53ELvA3AcP9aGkN…9c7TeeiQ
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.

4.492 Γ— 10⁹¹(92-digit number)
44921803626205691134…50810160224961041120
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
4.492 Γ— 10⁹¹(92-digit number)
44921803626205691134…50810160224961041119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.984 Γ— 10⁹¹(92-digit number)
89843607252411382269…01620320449922082239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.796 Γ— 10⁹²(93-digit number)
17968721450482276453…03240640899844164479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.593 Γ— 10⁹²(93-digit number)
35937442900964552907…06481281799688328959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.187 Γ— 10⁹²(93-digit number)
71874885801929105815…12962563599376657919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.437 Γ— 10⁹³(94-digit number)
14374977160385821163…25925127198753315839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.874 Γ— 10⁹³(94-digit number)
28749954320771642326…51850254397506631679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.749 Γ— 10⁹³(94-digit number)
57499908641543284652…03700508795013263359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.149 Γ— 10⁹⁴(95-digit number)
11499981728308656930…07401017590026526719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.299 Γ— 10⁹⁴(95-digit number)
22999963456617313861…14802035180053053439
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 275178

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 87fa6b64e3c4198b094a4eb6589c4712c3d8be0eadf68bcba5b0decbad8f380d

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 #275,178 on Chainz β†—
Circulating Supply:57,740,693 XPMΒ·at block #6,812,073 Β· updates every 60s
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