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Block #137,161

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2013, 3:46:03 PM Β· Difficulty 9.8198 Β· 6,679,009 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d9aa5467e1c0a18b8992735f6c1ddc79323396236dfa83c2a17e65347998f2c2
View on Chainz β†—

Height

#137,161

Difficulty

9.819846

Transactions

1

Size

196 B

Version

2

Bits

09d1e170

Nonce

144,876

Timestamp

8/27/2013, 3:46:03 PM

Confirmations

6,679,009

Merkle Root

e8f2c7ff1e5aac150551962173998251f95deade3f38346d70ddfb541627a786
Transactions (1)
Coinbasee8f2c7ff1e5aac…ddfb541627a786
1 in β†’ 1 out10.3500 XPM109 B
APhf7UNh…GDFABLcg
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.

3.200 Γ— 10⁸⁸(89-digit number)
32002344441143488293…34472860612254558400
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
3.200 Γ— 10⁸⁸(89-digit number)
32002344441143488293…34472860612254558399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.400 Γ— 10⁸⁸(89-digit number)
64004688882286976587…68945721224509116799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.280 Γ— 10⁸⁹(90-digit number)
12800937776457395317…37891442449018233599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.560 Γ— 10⁸⁹(90-digit number)
25601875552914790635…75782884898036467199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.120 Γ— 10⁸⁹(90-digit number)
51203751105829581270…51565769796072934399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.024 Γ— 10⁹⁰(91-digit number)
10240750221165916254…03131539592145868799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.048 Γ— 10⁹⁰(91-digit number)
20481500442331832508…06263079184291737599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.096 Γ— 10⁹⁰(91-digit number)
40963000884663665016…12526158368583475199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.192 Γ— 10⁹⁰(91-digit number)
81926001769327330032…25052316737166950399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.638 Γ— 10⁹¹(92-digit number)
16385200353865466006…50104633474333900799
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 137161

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 d9aa5467e1c0a18b8992735f6c1ddc79323396236dfa83c2a17e65347998f2c2

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 #137,161 on Chainz β†—
Circulating Supply:57,773,483 XPMΒ·at block #6,816,169 Β· updates every 60s
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