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Home/Chain Registry/Block #133,972

Block #133,972

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/25/2013, 7:42:15 PM Β· Difficulty 9.7991 Β· 6,678,617 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d2e40cec3890306017834d0f5d66dcc253f628d594e88d00a083489df9fe4b85
View on Chainz β†—

Height

#133,972

Difficulty

9.799128

Transactions

1

Size

200 B

Version

2

Bits

09cc93ae

Nonce

12,507

Timestamp

8/25/2013, 7:42:15 PM

Confirmations

6,678,617

Merkle Root

5e587b56ee267940134bb1d3dfc6b0bf6cb73196a628fcab3e230c6fc6add4e4
Transactions (1)
Coinbase5e587b56ee2679…230c6fc6add4e4
1 in β†’ 1 out10.4000 XPM109 B
AWsEijaA…9WbDL6tH
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.

7.406 Γ— 10⁹⁡(96-digit number)
74064780193128837711…07756514234059014000
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
7.406 Γ— 10⁹⁡(96-digit number)
74064780193128837711…07756514234059013999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.481 Γ— 10⁹⁢(97-digit number)
14812956038625767542…15513028468118027999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.962 Γ— 10⁹⁢(97-digit number)
29625912077251535084…31026056936236055999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.925 Γ— 10⁹⁢(97-digit number)
59251824154503070169…62052113872472111999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.185 Γ— 10⁹⁷(98-digit number)
11850364830900614033…24104227744944223999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.370 Γ— 10⁹⁷(98-digit number)
23700729661801228067…48208455489888447999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.740 Γ— 10⁹⁷(98-digit number)
47401459323602456135…96416910979776895999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.480 Γ— 10⁹⁷(98-digit number)
94802918647204912270…92833821959553791999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.896 Γ— 10⁹⁸(99-digit number)
18960583729440982454…85667643919107583999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.792 Γ— 10⁹⁸(99-digit number)
37921167458881964908…71335287838215167999
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 133972

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 d2e40cec3890306017834d0f5d66dcc253f628d594e88d00a083489df9fe4b85

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 #133,972 on Chainz β†—
Circulating Supply:57,744,746 XPMΒ·at block #6,812,588 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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