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Block #1,587,430

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/16/2016, 6:10:39 PM Β· Difficulty 10.6501 Β· 5,248,988 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
69f36b2fd6274fe620fef57dd21a00f79297935b8477f3930d207e7bdd62fd4c
View on Chainz β†—

Difficulty

10.650113

Transactions

1

Size

200 B

Version

2

Bits

0aa66dcb

Nonce

23,169,628

Timestamp

5/16/2016, 6:10:39 PM

Confirmations

5,248,988

Merkle Root

5d9c3f97092f00946bf4cbf8d146714ecec4dd780fb12768af0bc75641afd35d
Transactions (1)
Coinbase5d9c3f97092f00…0bc75641afd35d
1 in β†’ 1 out8.8000 XPM109 B
ALaTiuVg…vWJ3jYUb
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.

1.629 Γ— 10⁹⁢(97-digit number)
16299365396661111973…02513105955498009600
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.629 Γ— 10⁹⁢(97-digit number)
16299365396661111973…02513105955498009599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.259 Γ— 10⁹⁢(97-digit number)
32598730793322223947…05026211910996019199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.519 Γ— 10⁹⁢(97-digit number)
65197461586644447895…10052423821992038399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.303 Γ— 10⁹⁷(98-digit number)
13039492317328889579…20104847643984076799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.607 Γ— 10⁹⁷(98-digit number)
26078984634657779158…40209695287968153599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.215 Γ— 10⁹⁷(98-digit number)
52157969269315558316…80419390575936307199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.043 Γ— 10⁹⁸(99-digit number)
10431593853863111663…60838781151872614399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.086 Γ— 10⁹⁸(99-digit number)
20863187707726223326…21677562303745228799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.172 Γ— 10⁹⁸(99-digit number)
41726375415452446653…43355124607490457599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.345 Γ— 10⁹⁸(99-digit number)
83452750830904893306…86710249214980915199
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 1587430

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 69f36b2fd6274fe620fef57dd21a00f79297935b8477f3930d207e7bdd62fd4c

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 #1,587,430 on Chainz β†—
Circulating Supply:57,935,610 XPMΒ·at block #6,836,417 Β· updates every 60s
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