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Block #1,249,628

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/23/2015, 12:57:22 PM Β· Difficulty 10.7676 Β· 5,577,285 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f9bedf467cd0ab7a502e9168eabbeda876d3fc94876216b1c777c1787330c6b4
View on Chainz β†—

Difficulty

10.767598

Transactions

1

Size

201 B

Version

2

Bits

0ac48154

Nonce

521,970,366

Timestamp

9/23/2015, 12:57:22 PM

Confirmations

5,577,285

Merkle Root

9df6e56927538fbbacce224ef8d6e696d25d1bb525f81b2fe2222d3fed0ab19a
Transactions (1)
Coinbase9df6e56927538f…222d3fed0ab19a
1 in β†’ 1 out8.6100 XPM110 B
AKE9nGNk…CauC28fq
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.

7.739 Γ— 10⁹⁷(98-digit number)
77390930830254875788…84716388292708147200
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
7.739 Γ— 10⁹⁷(98-digit number)
77390930830254875788…84716388292708147201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.547 Γ— 10⁹⁸(99-digit number)
15478186166050975157…69432776585416294401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.095 Γ— 10⁹⁸(99-digit number)
30956372332101950315…38865553170832588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.191 Γ— 10⁹⁸(99-digit number)
61912744664203900630…77731106341665177601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.238 Γ— 10⁹⁹(100-digit number)
12382548932840780126…55462212683330355201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.476 Γ— 10⁹⁹(100-digit number)
24765097865681560252…10924425366660710401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.953 Γ— 10⁹⁹(100-digit number)
49530195731363120504…21848850733321420801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.906 Γ— 10⁹⁹(100-digit number)
99060391462726241009…43697701466642841601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.981 Γ— 10¹⁰⁰(101-digit number)
19812078292545248201…87395402933285683201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.962 Γ— 10¹⁰⁰(101-digit number)
39624156585090496403…74790805866571366401
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 1249628

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 f9bedf467cd0ab7a502e9168eabbeda876d3fc94876216b1c777c1787330c6b4

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 #1,249,628 on Chainz β†—
Circulating Supply:57,859,473 XPMΒ·at block #6,826,912 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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