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Block #1,534,792

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/10/2016, 11:40:07 AM Β· Difficulty 10.6182 Β· 5,276,918 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
be708e813fb1431a6bcb99a718576fe2023c71e6ae4eb98a4c7efc38a7d6459e
View on Chainz β†—

Difficulty

10.618246

Transactions

1

Size

243 B

Version

2

Bits

0a9e4557

Nonce

317,829,944

Timestamp

4/10/2016, 11:40:07 AM

Confirmations

5,276,918

Merkle Root

b42802529b04cb4ca2a8441db40034bff388a613ace4d80c5d3b7cc65189875d
Transactions (1)
Coinbaseb42802529b04cb…3b7cc65189875d
1 in β†’ 2 out8.8600 XPM152 B
AMZW7sdg…BUtLxkqyALPu3s2c…EJXLjVFh
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.

7.075 Γ— 10⁹⁡(96-digit number)
70750552495590405731…87610381987272537200
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
7.075 Γ— 10⁹⁡(96-digit number)
70750552495590405731…87610381987272537199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.415 Γ— 10⁹⁢(97-digit number)
14150110499118081146…75220763974545074399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.830 Γ— 10⁹⁢(97-digit number)
28300220998236162292…50441527949090148799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.660 Γ— 10⁹⁢(97-digit number)
56600441996472324585…00883055898180297599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.132 Γ— 10⁹⁷(98-digit number)
11320088399294464917…01766111796360595199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.264 Γ— 10⁹⁷(98-digit number)
22640176798588929834…03532223592721190399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.528 Γ— 10⁹⁷(98-digit number)
45280353597177859668…07064447185442380799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.056 Γ— 10⁹⁷(98-digit number)
90560707194355719336…14128894370884761599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.811 Γ— 10⁹⁸(99-digit number)
18112141438871143867…28257788741769523199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.622 Γ— 10⁹⁸(99-digit number)
36224282877742287734…56515577483539046399
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 1534792

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 be708e813fb1431a6bcb99a718576fe2023c71e6ae4eb98a4c7efc38a7d6459e

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 #1,534,792 on Chainz β†—
Circulating Supply:57,737,792 XPMΒ·at block #6,811,709 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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