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Home/Chain Registry/Block #1,578,098

Block #1,578,098

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/9/2016, 11:02:06 PM Β· Difficulty 10.6801 Β· 5,248,240 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
76d5ac0c515ea3692ddfb0cf4ffa9ed01f9eedb1a80798691912a4a51b21de3f
View on Chainz β†—

Difficulty

10.680058

Transactions

1

Size

201 B

Version

2

Bits

0aae184c

Nonce

1,320,045,171

Timestamp

5/9/2016, 11:02:06 PM

Confirmations

5,248,240

Merkle Root

8e4f7434f42c7755da16849901688d0c941d6d7ee0c77f83914573a5c99f3f3b
Transactions (1)
Coinbase8e4f7434f42c77…4573a5c99f3f3b
1 in β†’ 1 out8.7500 XPM110 B
ARqcvS7X…KeKayx75
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.

1.826 Γ— 10⁹⁢(97-digit number)
18265546435288712521…64117165116516730880
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
1.826 Γ— 10⁹⁢(97-digit number)
18265546435288712521…64117165116516730881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.653 Γ— 10⁹⁢(97-digit number)
36531092870577425042…28234330233033461761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.306 Γ— 10⁹⁢(97-digit number)
73062185741154850084…56468660466066923521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.461 Γ— 10⁹⁷(98-digit number)
14612437148230970016…12937320932133847041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.922 Γ— 10⁹⁷(98-digit number)
29224874296461940033…25874641864267694081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.844 Γ— 10⁹⁷(98-digit number)
58449748592923880067…51749283728535388161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.168 Γ— 10⁹⁸(99-digit number)
11689949718584776013…03498567457070776321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.337 Γ— 10⁹⁸(99-digit number)
23379899437169552027…06997134914141552641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.675 Γ— 10⁹⁸(99-digit number)
46759798874339104054…13994269828283105281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.351 Γ— 10⁹⁸(99-digit number)
93519597748678208108…27988539656566210561
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 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
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 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 1578098

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 76d5ac0c515ea3692ddfb0cf4ffa9ed01f9eedb1a80798691912a4a51b21de3f

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 #1,578,098 on Chainz β†—
Circulating Supply:57,854,846 XPMΒ·at block #6,826,337 Β· updates every 60s
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