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Block #1,587,427

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/16/2016, 6:05:32 PM Β· Difficulty 10.6501 Β· 5,243,579 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0c498b62c727f78b918c0899bfcbcb3bc3fa3e254bdb9455b807c447a6e3b91b
View on Chainz β†—

Difficulty

10.650121

Transactions

1

Size

200 B

Version

2

Bits

0aa66e51

Nonce

2,138,264,525

Timestamp

5/16/2016, 6:05:32 PM

Confirmations

5,243,579

Merkle Root

f1e7d9c9215832d31de81e4370d7ea63ef435cad89030691e7938a63105f8ae5
Transactions (1)
Coinbasef1e7d9c9215832…938a63105f8ae5
1 in β†’ 1 out8.8000 XPM109 B
ARtBYtbB…4uYvxD8k
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.

5.337 Γ— 10⁹⁢(97-digit number)
53372348768728303613…12659292420185984000
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
5.337 Γ— 10⁹⁢(97-digit number)
53372348768728303613…12659292420185984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.067 Γ— 10⁹⁷(98-digit number)
10674469753745660722…25318584840371968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.134 Γ— 10⁹⁷(98-digit number)
21348939507491321445…50637169680743936001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.269 Γ— 10⁹⁷(98-digit number)
42697879014982642890…01274339361487872001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.539 Γ— 10⁹⁷(98-digit number)
85395758029965285781…02548678722975744001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.707 Γ— 10⁹⁸(99-digit number)
17079151605993057156…05097357445951488001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.415 Γ— 10⁹⁸(99-digit number)
34158303211986114312…10194714891902976001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.831 Γ— 10⁹⁸(99-digit number)
68316606423972228625…20389429783805952001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.366 Γ— 10⁹⁹(100-digit number)
13663321284794445725…40778859567611904001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.732 Γ— 10⁹⁹(100-digit number)
27326642569588891450…81557719135223808001
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 1587427

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 0c498b62c727f78b918c0899bfcbcb3bc3fa3e254bdb9455b807c447a6e3b91b

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 #1,587,427 on Chainz β†—
Circulating Supply:57,892,190 XPMΒ·at block #6,831,005 Β· updates every 60s
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