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Home/Chain Registry/Block #1,613,789

Block #1,613,789

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/4/2016, 1:44:54 PM Β· Difficulty 10.5963 Β· 5,227,287 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4560a6e2a90f1f96da314fc656210a823cc2e76ed656968ae24ceab35b974ae1
View on Chainz β†—

Difficulty

10.596323

Transactions

1

Size

199 B

Version

2

Bits

0a98a89a

Nonce

151,780,626

Timestamp

6/4/2016, 1:44:54 PM

Confirmations

5,227,287

Merkle Root

c4837c39a80c021ef4e50f2db64e3eb0ea7b4fbbca7e78646513239801d16991
Transactions (1)
Coinbasec4837c39a80c02…13239801d16991
1 in β†’ 1 out8.8900 XPM109 B
AHFoLV82…5nCe7aoC
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.

8.854 Γ— 10⁹³(94-digit number)
88547982594191334906…34629109815206296320
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
8.854 Γ— 10⁹³(94-digit number)
88547982594191334906…34629109815206296319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.770 Γ— 10⁹⁴(95-digit number)
17709596518838266981…69258219630412592639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.541 Γ— 10⁹⁴(95-digit number)
35419193037676533962…38516439260825185279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.083 Γ— 10⁹⁴(95-digit number)
70838386075353067925…77032878521650370559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.416 Γ— 10⁹⁡(96-digit number)
14167677215070613585…54065757043300741119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.833 Γ— 10⁹⁡(96-digit number)
28335354430141227170…08131514086601482239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.667 Γ— 10⁹⁡(96-digit number)
56670708860282454340…16263028173202964479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.133 Γ— 10⁹⁢(97-digit number)
11334141772056490868…32526056346405928959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.266 Γ— 10⁹⁢(97-digit number)
22668283544112981736…65052112692811857919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.533 Γ— 10⁹⁢(97-digit number)
45336567088225963472…30104225385623715839
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 1613789

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 4560a6e2a90f1f96da314fc656210a823cc2e76ed656968ae24ceab35b974ae1

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 #1,613,789 on Chainz β†—
Circulating Supply:57,972,973 XPMΒ·at block #6,841,075 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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