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Block #90,301

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/31/2013, 12:39:07 AM Β· Difficulty 9.2472 Β· 6,707,879 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e8c013d2e60c5f10e0f5008cca652da7143761fbb16f518b6ac5e519e64c780b
View on Chainz β†—

Height

#90,301

Difficulty

9.247248

Transactions

1

Size

202 B

Version

2

Bits

093f4ba6

Nonce

390,414

Timestamp

7/31/2013, 12:39:07 AM

Confirmations

6,707,879

Merkle Root

69135e5f59550e3d1d4db3f65ef90c61de3928e3b0d09a8112e43a20336fd0e6
Transactions (1)
Coinbase69135e5f59550e…e43a20336fd0e6
1 in β†’ 1 out11.6800 XPM112 B
AT5A2KL6…CT16n6i2
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.

1.731 Γ— 10⁹⁡(96-digit number)
17314861270730876615…41010836322790494450
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
1.731 Γ— 10⁹⁡(96-digit number)
17314861270730876615…41010836322790494451
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.462 Γ— 10⁹⁡(96-digit number)
34629722541461753231…82021672645580988901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.925 Γ— 10⁹⁡(96-digit number)
69259445082923506462…64043345291161977801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.385 Γ— 10⁹⁢(97-digit number)
13851889016584701292…28086690582323955601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.770 Γ— 10⁹⁢(97-digit number)
27703778033169402584…56173381164647911201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.540 Γ— 10⁹⁢(97-digit number)
55407556066338805169…12346762329295822401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.108 Γ— 10⁹⁷(98-digit number)
11081511213267761033…24693524658591644801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.216 Γ— 10⁹⁷(98-digit number)
22163022426535522067…49387049317183289601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.432 Γ— 10⁹⁷(98-digit number)
44326044853071044135…98774098634366579201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 90301

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 e8c013d2e60c5f10e0f5008cca652da7143761fbb16f518b6ac5e519e64c780b

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 #90,301 on Chainz β†—
Circulating Supply:57,629,443 XPMΒ·at block #6,798,179 Β· updates every 60s
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