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Block #83,553

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/26/2013, 5:54:57 AM Β· Difficulty 9.2671 Β· 6,717,142 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fe1969004704227491d2a6748eeabe2d9a8a296b682e03b7f9281e383b4b218b
View on Chainz β†—

Height

#83,553

Difficulty

9.267083

Transactions

1

Size

200 B

Version

2

Bits

09445f8b

Nonce

167,835

Timestamp

7/26/2013, 5:54:57 AM

Confirmations

6,717,142

Merkle Root

95c90018fff6812d82882e4bbf0b61e2b65686fa6596b62945bfc82f7cfdfec3
Transactions (1)
Coinbase95c90018fff681…bfc82f7cfdfec3
1 in β†’ 1 out11.6300 XPM109 B
AcuJraLT…Y66BS47Q
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.

7.920 Γ— 10⁹⁷(98-digit number)
79207820804497602357…29421959483249335680
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
7.920 Γ— 10⁹⁷(98-digit number)
79207820804497602357…29421959483249335679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.584 Γ— 10⁹⁸(99-digit number)
15841564160899520471…58843918966498671359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.168 Γ— 10⁹⁸(99-digit number)
31683128321799040943…17687837932997342719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.336 Γ— 10⁹⁸(99-digit number)
63366256643598081886…35375675865994685439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.267 Γ— 10⁹⁹(100-digit number)
12673251328719616377…70751351731989370879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.534 Γ— 10⁹⁹(100-digit number)
25346502657439232754…41502703463978741759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.069 Γ— 10⁹⁹(100-digit number)
50693005314878465509…83005406927957483519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.013 Γ— 10¹⁰⁰(101-digit number)
10138601062975693101…66010813855914967039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.027 Γ— 10¹⁰⁰(101-digit number)
20277202125951386203…32021627711829934079
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 83553

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 fe1969004704227491d2a6748eeabe2d9a8a296b682e03b7f9281e383b4b218b

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 #83,553 on Chainz β†—
Circulating Supply:57,649,624 XPMΒ·at block #6,800,694 Β· updates every 60s
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