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Home/Chain Registry/Block #2,783,677

Block #2,783,677

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2018, 6:07:29 PM Β· Difficulty 11.6645 Β· 4,059,177 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f85296b820c5d61bf8f7a3d5ed4776617cb787fb82fe1f7114a5e55759b94656
View on Chainz β†—

Difficulty

11.664540

Transactions

1

Size

200 B

Version

2

Bits

0baa1f4c

Nonce

308,766,033

Timestamp

8/7/2018, 6:07:29 PM

Confirmations

4,059,177

Merkle Root

b45cb51389684b5f3a8fd292ae0d39f4c88a7d6123f5fdaf069d047fc5b2b34b
Transactions (1)
Coinbaseb45cb51389684b…9d047fc5b2b34b
1 in β†’ 1 out7.3400 XPM110 B
AP4LkcaD…1V3S2TN8
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.

1.631 Γ— 10⁹⁡(96-digit number)
16317494792754917935…90461487846499947600
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
1.631 Γ— 10⁹⁡(96-digit number)
16317494792754917935…90461487846499947599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.263 Γ— 10⁹⁡(96-digit number)
32634989585509835871…80922975692999895199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.526 Γ— 10⁹⁡(96-digit number)
65269979171019671743…61845951385999790399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.305 Γ— 10⁹⁢(97-digit number)
13053995834203934348…23691902771999580799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.610 Γ— 10⁹⁢(97-digit number)
26107991668407868697…47383805543999161599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.221 Γ— 10⁹⁢(97-digit number)
52215983336815737394…94767611087998323199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.044 Γ— 10⁹⁷(98-digit number)
10443196667363147478…89535222175996646399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.088 Γ— 10⁹⁷(98-digit number)
20886393334726294957…79070444351993292799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.177 Γ— 10⁹⁷(98-digit number)
41772786669452589915…58140888703986585599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.354 Γ— 10⁹⁷(98-digit number)
83545573338905179831…16281777407973171199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.670 Γ— 10⁹⁸(99-digit number)
16709114667781035966…32563554815946342399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2783677

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 f85296b820c5d61bf8f7a3d5ed4776617cb787fb82fe1f7114a5e55759b94656

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 #2,783,677 on Chainz β†—
Circulating Supply:57,987,178 XPMΒ·at block #6,842,853 Β· updates every 60s
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