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Block #909,080

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/25/2015, 7:06:57 AM Β· Difficulty 10.9344 Β· 5,916,374 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d211edf2e1d72e3f543e4565cebcaf82b74891aa4f3fc06c3ec9a3f97a630413
View on Chainz β†—

Height

#909,080

Difficulty

10.934446

Transactions

1

Size

206 B

Version

2

Bits

0aef37d4

Nonce

739,081,510

Timestamp

1/25/2015, 7:06:57 AM

Confirmations

5,916,374

Merkle Root

87bfb10bf540c95ddcc0bbdefa858c2e51eab29a53e222a156fd6f1eb502b978
Transactions (1)
Coinbase87bfb10bf540c9…fd6f1eb502b978
1 in β†’ 1 out8.3500 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.468 Γ— 10⁹⁡(96-digit number)
14689551130290019841…36686633137378891520
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
1.468 Γ— 10⁹⁡(96-digit number)
14689551130290019841…36686633137378891521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.937 Γ— 10⁹⁡(96-digit number)
29379102260580039682…73373266274757783041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.875 Γ— 10⁹⁡(96-digit number)
58758204521160079365…46746532549515566081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.175 Γ— 10⁹⁢(97-digit number)
11751640904232015873…93493065099031132161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.350 Γ— 10⁹⁢(97-digit number)
23503281808464031746…86986130198062264321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.700 Γ— 10⁹⁢(97-digit number)
47006563616928063492…73972260396124528641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.401 Γ— 10⁹⁢(97-digit number)
94013127233856126984…47944520792249057281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.880 Γ— 10⁹⁷(98-digit number)
18802625446771225396…95889041584498114561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.760 Γ— 10⁹⁷(98-digit number)
37605250893542450793…91778083168996229121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.521 Γ— 10⁹⁷(98-digit number)
75210501787084901587…83556166337992458241
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 909080

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 d211edf2e1d72e3f543e4565cebcaf82b74891aa4f3fc06c3ec9a3f97a630413

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 #909,080 on Chainz β†—
Circulating Supply:57,847,737 XPMΒ·at block #6,825,453 Β· updates every 60s
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