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Block #337,106

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/31/2013, 10:31:46 AM Β· Difficulty 10.1392 Β· 6,487,455 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fbe568af557e8efee94b50d511d1bd31cf66923d55fc457324c403e245a99f6a
View on Chainz β†—

Height

#337,106

Difficulty

10.139172

Transactions

1

Size

189 B

Version

2

Bits

0a23a0c0

Nonce

2,806

Timestamp

12/31/2013, 10:31:46 AM

Confirmations

6,487,455

Merkle Root

733064853381eca652b7e8231cc281324a9ba9a746e741004dc0186bbc675d30
Transactions (1)
Coinbase733064853381ec…c0186bbc675d30
1 in β†’ 1 out9.7100 XPM97 B
AbMAHMS8…MwEzMSoj
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.

4.572 Γ— 10⁹⁹(100-digit number)
45724152478587487871…07595474781738729950
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
4.572 Γ— 10⁹⁹(100-digit number)
45724152478587487871…07595474781738729951
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.144 Γ— 10⁹⁹(100-digit number)
91448304957174975743…15190949563477459901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.828 Γ— 10¹⁰⁰(101-digit number)
18289660991434995148…30381899126954919801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.657 Γ— 10¹⁰⁰(101-digit number)
36579321982869990297…60763798253909839601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.315 Γ— 10¹⁰⁰(101-digit number)
73158643965739980594…21527596507819679201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.463 Γ— 10¹⁰¹(102-digit number)
14631728793147996118…43055193015639358401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.926 Γ— 10¹⁰¹(102-digit number)
29263457586295992237…86110386031278716801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.852 Γ— 10¹⁰¹(102-digit number)
58526915172591984475…72220772062557433601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.170 Γ— 10¹⁰²(103-digit number)
11705383034518396895…44441544125114867201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.341 Γ— 10¹⁰²(103-digit number)
23410766069036793790…88883088250229734401
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 337106

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 fbe568af557e8efee94b50d511d1bd31cf66923d55fc457324c403e245a99f6a

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 #337,106 on Chainz β†—
Circulating Supply:57,840,552 XPMΒ·at block #6,824,560 Β· updates every 60s
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