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Block #901,230

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/19/2015, 10:08:08 AM Β· Difficulty 10.9417 Β· 5,895,876 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
474cb6e68773d17240cc439b6f335522a275c284d8ad10243700f2929bb41a65
View on Chainz β†—

Height

#901,230

Difficulty

10.941680

Transactions

1

Size

243 B

Version

2

Bits

0af111f9

Nonce

35,453,280

Timestamp

1/19/2015, 10:08:08 AM

Confirmations

5,895,876

Merkle Root

2b3e74fa4d73ec6459527597524803707d9ddd7fa37e4723897b32d569cd2173
Transactions (1)
Coinbase2b3e74fa4d73ec…7b32d569cd2173
1 in β†’ 2 out8.3400 XPM152 B
AQXNNLgc…kBjowpEwALPu3s2c…EJXLjVFh
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.

1.071 Γ— 10⁹⁷(98-digit number)
10715379307888283247…85773496454185484800
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
1.071 Γ— 10⁹⁷(98-digit number)
10715379307888283247…85773496454185484801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.143 Γ— 10⁹⁷(98-digit number)
21430758615776566495…71546992908370969601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.286 Γ— 10⁹⁷(98-digit number)
42861517231553132991…43093985816741939201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.572 Γ— 10⁹⁷(98-digit number)
85723034463106265983…86187971633483878401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.714 Γ— 10⁹⁸(99-digit number)
17144606892621253196…72375943266967756801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.428 Γ— 10⁹⁸(99-digit number)
34289213785242506393…44751886533935513601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.857 Γ— 10⁹⁸(99-digit number)
68578427570485012786…89503773067871027201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.371 Γ— 10⁹⁹(100-digit number)
13715685514097002557…79007546135742054401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.743 Γ— 10⁹⁹(100-digit number)
27431371028194005114…58015092271484108801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.486 Γ— 10⁹⁹(100-digit number)
54862742056388010229…16030184542968217601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.097 Γ— 10¹⁰⁰(101-digit number)
10972548411277602045…32060369085936435201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 901230

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 474cb6e68773d17240cc439b6f335522a275c284d8ad10243700f2929bb41a65

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 #901,230 on Chainz β†—
Circulating Supply:57,620,870 XPMΒ·at block #6,797,105 Β· updates every 60s
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