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Block #160,989

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/12/2013, 8:38:19 AM Β· Difficulty 9.8594 Β· 6,655,088 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6a1ce2aa18089c1dba8836ab743ee955be5ad0bb55d76de6676999bf14d2fe8e
View on Chainz β†—

Height

#160,989

Difficulty

9.859434

Transactions

1

Size

199 B

Version

2

Bits

09dc03d8

Nonce

359,805

Timestamp

9/12/2013, 8:38:19 AM

Confirmations

6,655,088

Merkle Root

650bd8a2e00575197a8cef93d3da00785ab745e262c93b6c93fd067f0ce4fa76
Transactions (1)
Coinbase650bd8a2e00575…fd067f0ce4fa76
1 in β†’ 1 out10.2700 XPM109 B
AP52EE3F…ZhqfNP3e
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.

5.090 Γ— 10⁹³(94-digit number)
50906802667909548182…10554843681729599000
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
5.090 Γ— 10⁹³(94-digit number)
50906802667909548182…10554843681729598999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.018 Γ— 10⁹⁴(95-digit number)
10181360533581909636…21109687363459197999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.036 Γ— 10⁹⁴(95-digit number)
20362721067163819273…42219374726918395999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.072 Γ— 10⁹⁴(95-digit number)
40725442134327638546…84438749453836791999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.145 Γ— 10⁹⁴(95-digit number)
81450884268655277092…68877498907673583999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.629 Γ— 10⁹⁡(96-digit number)
16290176853731055418…37754997815347167999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.258 Γ— 10⁹⁡(96-digit number)
32580353707462110836…75509995630694335999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.516 Γ— 10⁹⁡(96-digit number)
65160707414924221673…51019991261388671999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.303 Γ— 10⁹⁢(97-digit number)
13032141482984844334…02039982522777343999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 160989

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 6a1ce2aa18089c1dba8836ab743ee955be5ad0bb55d76de6676999bf14d2fe8e

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 #160,989 on Chainz β†—
Circulating Supply:57,772,734 XPMΒ·at block #6,816,076 Β· updates every 60s
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