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Block #357,387

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/13/2014, 9:16:39 AM Β· Difficulty 10.3841 Β· 6,443,604 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2b612989e0041eb42284f072043f87ce8fb71d0314efd4eb4b90d3c98cba4b71
View on Chainz β†—

Height

#357,387

Difficulty

10.384136

Transactions

1

Size

202 B

Version

2

Bits

0a6256b9

Nonce

70,911

Timestamp

1/13/2014, 9:16:39 AM

Confirmations

6,443,604

Merkle Root

5b3d8a7b307e80eae10ef638660cf8a09b7b28f1631d341582522ed3cc6c08a3
Transactions (1)
Coinbase5b3d8a7b307e80…522ed3cc6c08a3
1 in β†’ 1 out9.2600 XPM110 B
AeKNrjNj…1NEq95Ta
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.

8.651 Γ— 10⁹⁸(99-digit number)
86515385124895832453…36617678638263549760
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
8.651 Γ— 10⁹⁸(99-digit number)
86515385124895832453…36617678638263549761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.730 Γ— 10⁹⁹(100-digit number)
17303077024979166490…73235357276527099521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.460 Γ— 10⁹⁹(100-digit number)
34606154049958332981…46470714553054199041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.921 Γ— 10⁹⁹(100-digit number)
69212308099916665962…92941429106108398081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.384 Γ— 10¹⁰⁰(101-digit number)
13842461619983333192…85882858212216796161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.768 Γ— 10¹⁰⁰(101-digit number)
27684923239966666385…71765716424433592321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.536 Γ— 10¹⁰⁰(101-digit number)
55369846479933332770…43531432848867184641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.107 Γ— 10¹⁰¹(102-digit number)
11073969295986666554…87062865697734369281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.214 Γ— 10¹⁰¹(102-digit number)
22147938591973333108…74125731395468738561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.429 Γ— 10¹⁰¹(102-digit number)
44295877183946666216…48251462790937477121
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 357387

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 2b612989e0041eb42284f072043f87ce8fb71d0314efd4eb4b90d3c98cba4b71

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 #357,387 on Chainz β†—
Circulating Supply:57,651,988 XPMΒ·at block #6,800,990 Β· updates every 60s
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