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Block #21,615

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/12/2013, 2:59:28 PM Β· Difficulty 7.9453 Β· 6,804,856 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
815710627d86502e70603bf3e15b98f5708a55df93c22acbbdabc1d3fb7246f9
View on Chainz β†—

Height

#21,615

Difficulty

7.945309

Transactions

1

Size

196 B

Version

2

Bits

07f1ffc7

Nonce

80

Timestamp

7/12/2013, 2:59:28 PM

Confirmations

6,804,856

Merkle Root

d101b750b1ca4c1de4ac7297878a8efd83747f39cda6d6fa5b8cfe3e25a8e687
Transactions (1)
Coinbased101b750b1ca4c…8cfe3e25a8e687
1 in β†’ 1 out15.8200 XPM108 B
AcmT3PEH…Ai3piMoG
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.

1.765 Γ— 10⁹⁰(91-digit number)
17650864184166426942…47858553391064487660
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
1.765 Γ— 10⁹⁰(91-digit number)
17650864184166426942…47858553391064487659
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.530 Γ— 10⁹⁰(91-digit number)
35301728368332853884…95717106782128975319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.060 Γ— 10⁹⁰(91-digit number)
70603456736665707769…91434213564257950639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.412 Γ— 10⁹¹(92-digit number)
14120691347333141553…82868427128515901279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.824 Γ— 10⁹¹(92-digit number)
28241382694666283107…65736854257031802559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.648 Γ— 10⁹¹(92-digit number)
56482765389332566215…31473708514063605119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.129 Γ— 10⁹²(93-digit number)
11296553077866513243…62947417028127210239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.259 Γ— 10⁹²(93-digit number)
22593106155733026486…25894834056254420479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 21615

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 815710627d86502e70603bf3e15b98f5708a55df93c22acbbdabc1d3fb7246f9

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 #21,615 on Chainz β†—
Circulating Supply:57,855,908 XPMΒ·at block #6,826,470 Β· updates every 60s
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