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Home/Chain Registry/Block #1,281,901

Block #1,281,901

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/14/2015, 3:43:59 PM Β· Difficulty 10.8404 Β· 5,512,914 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ae4e3a7f9ccbfa84b1d0ab8e4ffa13bd5f9a7f3f08da54c72169e28c89ff521f
View on Chainz β†—

Difficulty

10.840417

Transactions

1

Size

207 B

Version

2

Bits

0ad72593

Nonce

2,506,317,823

Timestamp

10/14/2015, 3:43:59 PM

Confirmations

5,512,914

Merkle Root

8b0c5862c84ababde55862b0f5596040c8bb00f8d7f07299962896ad98df2094
Transactions (1)
Coinbase8b0c5862c84aba…2896ad98df2094
1 in β†’ 1 out8.5000 XPM116 B
AJCEY9yy…tg97E6zm
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.

8.203 Γ— 10⁹⁷(98-digit number)
82031097656034578775…13679432477071718400
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
8.203 Γ— 10⁹⁷(98-digit number)
82031097656034578775…13679432477071718399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.640 Γ— 10⁹⁸(99-digit number)
16406219531206915755…27358864954143436799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.281 Γ— 10⁹⁸(99-digit number)
32812439062413831510…54717729908286873599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.562 Γ— 10⁹⁸(99-digit number)
65624878124827663020…09435459816573747199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.312 Γ— 10⁹⁹(100-digit number)
13124975624965532604…18870919633147494399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.624 Γ— 10⁹⁹(100-digit number)
26249951249931065208…37741839266294988799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.249 Γ— 10⁹⁹(100-digit number)
52499902499862130416…75483678532589977599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.049 Γ— 10¹⁰⁰(101-digit number)
10499980499972426083…50967357065179955199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.099 Γ— 10¹⁰⁰(101-digit number)
20999960999944852166…01934714130359910399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.199 Γ— 10¹⁰⁰(101-digit number)
41999921999889704333…03869428260719820799
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 1281901

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 ae4e3a7f9ccbfa84b1d0ab8e4ffa13bd5f9a7f3f08da54c72169e28c89ff521f

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 #1,281,901 on Chainz β†—
Circulating Supply:57,602,567 XPMΒ·at block #6,794,814 Β· updates every 60s
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