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Block #668,521

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2014, 7:29:38 AM Β· Difficulty 10.9636 Β· 6,171,947 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3a406cb5a0fa6d937369cc4b9e5782c6957daf78472a257d2b30108da056683f
View on Chainz β†—

Height

#668,521

Difficulty

10.963598

Transactions

1

Size

207 B

Version

2

Bits

0af6ae57

Nonce

563,564,549

Timestamp

8/8/2014, 7:29:38 AM

Confirmations

6,171,947

Merkle Root

8f07f85166e3c26ca8ff4fe1887762f9b253cf85570df17f9740b6e156861c6d
Transactions (1)
Coinbase8f07f85166e3c2…40b6e156861c6d
1 in β†’ 1 out8.3100 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.

3.675 Γ— 10⁹⁷(98-digit number)
36752406328560601703…67334503790706528000
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
3.675 Γ— 10⁹⁷(98-digit number)
36752406328560601703…67334503790706527999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.350 Γ— 10⁹⁷(98-digit number)
73504812657121203407…34669007581413055999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.470 Γ— 10⁹⁸(99-digit number)
14700962531424240681…69338015162826111999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.940 Γ— 10⁹⁸(99-digit number)
29401925062848481363…38676030325652223999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.880 Γ— 10⁹⁸(99-digit number)
58803850125696962726…77352060651304447999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.176 Γ— 10⁹⁹(100-digit number)
11760770025139392545…54704121302608895999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.352 Γ— 10⁹⁹(100-digit number)
23521540050278785090…09408242605217791999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.704 Γ— 10⁹⁹(100-digit number)
47043080100557570180…18816485210435583999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.408 Γ— 10⁹⁹(100-digit number)
94086160201115140361…37632970420871167999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.881 Γ— 10¹⁰⁰(101-digit number)
18817232040223028072…75265940841742335999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.763 Γ— 10¹⁰⁰(101-digit number)
37634464080446056144…50531881683484671999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 668521

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 3a406cb5a0fa6d937369cc4b9e5782c6957daf78472a257d2b30108da056683f

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 #668,521 on Chainz β†—
Circulating Supply:57,968,073 XPMΒ·at block #6,840,467 Β· updates every 60s
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