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Block #297,649

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/6/2013, 5:57:48 PM Β· Difficulty 9.9920 Β· 6,516,574 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9be50c4dbf01a3d7a64ac97fc196f235f41aa34e90256f53d99181fe33ee3f12
View on Chainz β†—

Height

#297,649

Difficulty

9.992014

Transactions

1

Size

210 B

Version

2

Bits

09fdf4a0

Nonce

1,374

Timestamp

12/6/2013, 5:57:48 PM

Confirmations

6,516,574

Merkle Root

e04b66de073b8cb70c7312b7e2e1b80073b46c1e138108ea8ebeb1db2175f3f1
Transactions (1)
Coinbasee04b66de073b8c…beb1db2175f3f1
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.

1.014 Γ— 10¹⁰⁡(106-digit number)
10143330575973471920…25623563254575923200
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.014 Γ— 10¹⁰⁡(106-digit number)
10143330575973471920…25623563254575923201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.028 Γ— 10¹⁰⁡(106-digit number)
20286661151946943841…51247126509151846401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.057 Γ— 10¹⁰⁡(106-digit number)
40573322303893887682…02494253018303692801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.114 Γ— 10¹⁰⁡(106-digit number)
81146644607787775365…04988506036607385601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.622 Γ— 10¹⁰⁢(107-digit number)
16229328921557555073…09977012073214771201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.245 Γ— 10¹⁰⁢(107-digit number)
32458657843115110146…19954024146429542401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.491 Γ— 10¹⁰⁢(107-digit number)
64917315686230220292…39908048292859084801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.298 Γ— 10¹⁰⁷(108-digit number)
12983463137246044058…79816096585718169601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.596 Γ— 10¹⁰⁷(108-digit number)
25966926274492088116…59632193171436339201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.193 Γ— 10¹⁰⁷(108-digit number)
51933852548984176233…19264386342872678401
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 297649

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 9be50c4dbf01a3d7a64ac97fc196f235f41aa34e90256f53d99181fe33ee3f12

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 #297,649 on Chainz β†—
Circulating Supply:57,757,854 XPMΒ·at block #6,814,222 Β· updates every 60s
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