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Block #285,132

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/30/2013, 9:33:55 AM Β· Difficulty 9.9838 Β· 6,510,259 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
880a53b2f94e830dcc0bf3d34de52cf6b0be5d5a27e2c67ba6afe4d127c757ee
View on Chainz β†—

Height

#285,132

Difficulty

9.983784

Transactions

1

Size

208 B

Version

2

Bits

09fbd940

Nonce

17,423

Timestamp

11/30/2013, 9:33:55 AM

Confirmations

6,510,259

Merkle Root

4dd674b6270255b3e55622ddbc0ecbfacdb20433441d7b38ef709f567e3a8368
Transactions (1)
Coinbase4dd674b6270255…709f567e3a8368
1 in β†’ 1 out10.0200 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.499 Γ— 10¹⁰⁰(101-digit number)
14990684275937134539…96096424626238586880
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
1.499 Γ— 10¹⁰⁰(101-digit number)
14990684275937134539…96096424626238586881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.998 Γ— 10¹⁰⁰(101-digit number)
29981368551874269079…92192849252477173761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.996 Γ— 10¹⁰⁰(101-digit number)
59962737103748538158…84385698504954347521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.199 Γ— 10¹⁰¹(102-digit number)
11992547420749707631…68771397009908695041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.398 Γ— 10¹⁰¹(102-digit number)
23985094841499415263…37542794019817390081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.797 Γ— 10¹⁰¹(102-digit number)
47970189682998830526…75085588039634780161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.594 Γ— 10¹⁰¹(102-digit number)
95940379365997661053…50171176079269560321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.918 Γ— 10¹⁰²(103-digit number)
19188075873199532210…00342352158539120641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.837 Γ— 10¹⁰²(103-digit number)
38376151746399064421…00684704317078241281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.675 Γ— 10¹⁰²(103-digit number)
76752303492798128843…01369408634156482561
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 285132

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 880a53b2f94e830dcc0bf3d34de52cf6b0be5d5a27e2c67ba6afe4d127c757ee

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 #285,132 on Chainz β†—
Circulating Supply:57,607,188 XPMΒ·at block #6,795,390 Β· updates every 60s
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