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Home/Chain Registry/Block #2,770,933

Block #2,770,933

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/29/2018, 10:46:00 PM Β· Difficulty 11.6600 Β· 4,071,383 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
43f68a795aabc0342d073bc4d4b8367e280c08cc0052dc0037267fe50c58a8eb
View on Chainz β†—

Difficulty

11.660004

Transactions

2

Size

392 B

Version

2

Bits

0ba8f5fe

Nonce

638,715,359

Timestamp

7/29/2018, 10:46:00 PM

Confirmations

4,071,383

Merkle Root

63fa23613bac758e292a672bcecb829ba4cba66feda749a368a5641205a49171
Transactions (2)
Coinbase9c4ef87a75a638…976ba6cc49e979
1 in β†’ 1 out7.3500 XPM110 B
ARrXPAEJ…C43U72cQ
842d6c8934f17d…86e93b90d4e698
1 in β†’ 2 out7.4100 XPM192 B
ASmmPSo6…SeqbKzWNAU75oAQQ…qBZ98kJK
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.

2.059 Γ— 10⁹⁴(95-digit number)
20591622499931528546…93334069526941988290
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
2.059 Γ— 10⁹⁴(95-digit number)
20591622499931528546…93334069526941988289
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.118 Γ— 10⁹⁴(95-digit number)
41183244999863057093…86668139053883976579
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.236 Γ— 10⁹⁴(95-digit number)
82366489999726114186…73336278107767953159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.647 Γ— 10⁹⁡(96-digit number)
16473297999945222837…46672556215535906319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.294 Γ— 10⁹⁡(96-digit number)
32946595999890445674…93345112431071812639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.589 Γ— 10⁹⁡(96-digit number)
65893191999780891348…86690224862143625279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.317 Γ— 10⁹⁢(97-digit number)
13178638399956178269…73380449724287250559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.635 Γ— 10⁹⁢(97-digit number)
26357276799912356539…46760899448574501119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.271 Γ— 10⁹⁢(97-digit number)
52714553599824713079…93521798897149002239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.054 Γ— 10⁹⁷(98-digit number)
10542910719964942615…87043597794298004479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.108 Γ— 10⁹⁷(98-digit number)
21085821439929885231…74087195588596008959
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 2770933

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 43f68a795aabc0342d073bc4d4b8367e280c08cc0052dc0037267fe50c58a8eb

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 #2,770,933 on Chainz β†—
Circulating Supply:57,982,935 XPMΒ·at block #6,842,315 Β· updates every 60s
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