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Home/Chain Registry/Block #294,913

Block #294,913

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/5/2013, 3:47:39 AM Β· Difficulty 9.9912 Β· 6,531,707 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2be2f19b2f6e50955ae61711aa60ef0eeb521b0ef3af0410bfbacfc4fe63b296
View on Chainz β†—

Height

#294,913

Difficulty

9.991179

Transactions

1

Size

208 B

Version

2

Bits

09fdbde5

Nonce

156,043

Timestamp

12/5/2013, 3:47:39 AM

Confirmations

6,531,707

Merkle Root

03a78db747e0fc35184c0d54e82ba0ac840294390129eac9a4b1800e509659f0
Transactions (1)
Coinbase03a78db747e0fc…b1800e509659f0
1 in β†’ 1 out10.0000 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.013 Γ— 10⁹⁹(100-digit number)
10131139337780940999…03630237543725905920
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
1.013 Γ— 10⁹⁹(100-digit number)
10131139337780940999…03630237543725905919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.026 Γ— 10⁹⁹(100-digit number)
20262278675561881998…07260475087451811839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.052 Γ— 10⁹⁹(100-digit number)
40524557351123763996…14520950174903623679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.104 Γ— 10⁹⁹(100-digit number)
81049114702247527993…29041900349807247359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.620 Γ— 10¹⁰⁰(101-digit number)
16209822940449505598…58083800699614494719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.241 Γ— 10¹⁰⁰(101-digit number)
32419645880899011197…16167601399228989439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.483 Γ— 10¹⁰⁰(101-digit number)
64839291761798022394…32335202798457978879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.296 Γ— 10¹⁰¹(102-digit number)
12967858352359604478…64670405596915957759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.593 Γ— 10¹⁰¹(102-digit number)
25935716704719208957…29340811193831915519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.187 Γ— 10¹⁰¹(102-digit number)
51871433409438417915…58681622387663831039
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 294913

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 2be2f19b2f6e50955ae61711aa60ef0eeb521b0ef3af0410bfbacfc4fe63b296

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 #294,913 on Chainz β†—
Circulating Supply:57,857,113 XPMΒ·at block #6,826,619 Β· updates every 60s
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