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Home/Chain Registry/Block #2,784,163

Block #2,784,163

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/8/2018, 1:48:32 AM Β· Difficulty 11.6662 Β· 4,055,092 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
17eb640a0076f40fa115074ccb7067c2a72027f66c411f5b52ec90ecf0ece586
View on Chainz β†—

Difficulty

11.666212

Transactions

1

Size

201 B

Version

2

Bits

0baa8ce4

Nonce

1,725,136,789

Timestamp

8/8/2018, 1:48:32 AM

Confirmations

4,055,092

Merkle Root

b1e51caf92a81500e9bcd97d4e717803677600c9ecb5c1d96b8fa2c12c96cbf8
Transactions (1)
Coinbaseb1e51caf92a815…8fa2c12c96cbf8
1 in β†’ 1 out7.3400 XPM110 B
AHEhZvxc…4BYGKp1u
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.

7.473 Γ— 10⁹⁢(97-digit number)
74735755059040064236…46909640320598318080
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
7.473 Γ— 10⁹⁢(97-digit number)
74735755059040064236…46909640320598318081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.494 Γ— 10⁹⁷(98-digit number)
14947151011808012847…93819280641196636161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.989 Γ— 10⁹⁷(98-digit number)
29894302023616025694…87638561282393272321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.978 Γ— 10⁹⁷(98-digit number)
59788604047232051389…75277122564786544641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.195 Γ— 10⁹⁸(99-digit number)
11957720809446410277…50554245129573089281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.391 Γ— 10⁹⁸(99-digit number)
23915441618892820555…01108490259146178561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.783 Γ— 10⁹⁸(99-digit number)
47830883237785641111…02216980518292357121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.566 Γ— 10⁹⁸(99-digit number)
95661766475571282223…04433961036584714241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.913 Γ— 10⁹⁹(100-digit number)
19132353295114256444…08867922073169428481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.826 Γ— 10⁹⁹(100-digit number)
38264706590228512889…17735844146338856961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.652 Γ— 10⁹⁹(100-digit number)
76529413180457025778…35471688292677713921
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2784163

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 17eb640a0076f40fa115074ccb7067c2a72027f66c411f5b52ec90ecf0ece586

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 #2,784,163 on Chainz β†—
Circulating Supply:57,958,323 XPMΒ·at block #6,839,254 Β· updates every 60s
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