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Block #1,681,651

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2016, 11:51:19 AM Β· Difficulty 10.7165 Β· 5,156,557 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cc55133d32e7feaaf171238b1f392921e82596df3cb4347a6d1c4f0209a606b2
View on Chainz β†—

Difficulty

10.716487

Transactions

1

Size

200 B

Version

2

Bits

0ab76bb9

Nonce

138,992,328

Timestamp

7/20/2016, 11:51:19 AM

Confirmations

5,156,557

Merkle Root

d6b50802aa4b990b5222f923898a5ebd0a0e338efcaba725f16e8938f2ce53e3
Transactions (1)
Coinbased6b50802aa4b99…6e8938f2ce53e3
1 in β†’ 1 out8.6900 XPM109 B
AJJfWrN2…CfBWYtuz
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.

1.470 Γ— 10⁹⁷(98-digit number)
14709348279853639867…43354991687544012800
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
1.470 Γ— 10⁹⁷(98-digit number)
14709348279853639867…43354991687544012799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.941 Γ— 10⁹⁷(98-digit number)
29418696559707279734…86709983375088025599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.883 Γ— 10⁹⁷(98-digit number)
58837393119414559468…73419966750176051199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.176 Γ— 10⁹⁸(99-digit number)
11767478623882911893…46839933500352102399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.353 Γ— 10⁹⁸(99-digit number)
23534957247765823787…93679867000704204799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.706 Γ— 10⁹⁸(99-digit number)
47069914495531647574…87359734001408409599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.413 Γ— 10⁹⁸(99-digit number)
94139828991063295149…74719468002816819199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.882 Γ— 10⁹⁹(100-digit number)
18827965798212659029…49438936005633638399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.765 Γ— 10⁹⁹(100-digit number)
37655931596425318059…98877872011267276799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.531 Γ— 10⁹⁹(100-digit number)
75311863192850636119…97755744022534553599
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 1681651

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 cc55133d32e7feaaf171238b1f392921e82596df3cb4347a6d1c4f0209a606b2

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 #1,681,651 on Chainz β†—
Circulating Supply:57,949,937 XPMΒ·at block #6,838,207 Β· updates every 60s
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