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Home/Chain Registry/Block #1,613,449

Block #1,613,449

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/4/2016, 7:30:52 AM Β· Difficulty 10.5991 Β· 5,228,554 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a9d5aa4c814e693e3c3f5292bd1de6fd4a4a5931bc75739f5db3ae6f4459c1c1
View on Chainz β†—

Difficulty

10.599055

Transactions

1

Size

201 B

Version

2

Bits

0a995bad

Nonce

1,637,557,684

Timestamp

6/4/2016, 7:30:52 AM

Confirmations

5,228,554

Merkle Root

ffe8d0527a1d1266e325d282db2c656e30ec3075e7d9110bccaad99d4dae2ac7
Transactions (1)
Coinbaseffe8d0527a1d12…aad99d4dae2ac7
1 in β†’ 1 out8.8900 XPM110 B
AYgWEVKc…ciwwS34y
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.

5.968 Γ— 10⁹⁢(97-digit number)
59680740718889650769…96894700937845098880
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
5.968 Γ— 10⁹⁢(97-digit number)
59680740718889650769…96894700937845098879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.193 Γ— 10⁹⁷(98-digit number)
11936148143777930153…93789401875690197759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.387 Γ— 10⁹⁷(98-digit number)
23872296287555860307…87578803751380395519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.774 Γ— 10⁹⁷(98-digit number)
47744592575111720615…75157607502760791039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.548 Γ— 10⁹⁷(98-digit number)
95489185150223441230…50315215005521582079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.909 Γ— 10⁹⁸(99-digit number)
19097837030044688246…00630430011043164159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.819 Γ— 10⁹⁸(99-digit number)
38195674060089376492…01260860022086328319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.639 Γ— 10⁹⁸(99-digit number)
76391348120178752984…02521720044172656639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.527 Γ— 10⁹⁹(100-digit number)
15278269624035750596…05043440088345313279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.055 Γ— 10⁹⁹(100-digit number)
30556539248071501193…10086880176690626559
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 1613449

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 a9d5aa4c814e693e3c3f5292bd1de6fd4a4a5931bc75739f5db3ae6f4459c1c1

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 #1,613,449 on Chainz β†—
Circulating Supply:57,980,408 XPMΒ·at block #6,842,002 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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