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Block #1,534,675

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2016, 9:50:49 AM Β· Difficulty 10.6175 Β· 5,280,183 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ecc5146684873155c4dfd5d67423bad6c20dd3b672ebe7d7a1a4eb21cb2241fc
View on Chainz β†—

Difficulty

10.617478

Transactions

1

Size

243 B

Version

2

Bits

0a9e1304

Nonce

198,401,377

Timestamp

4/10/2016, 9:50:49 AM

Confirmations

5,280,183

Merkle Root

ae3fed37442a19bbee126fb677dfa57fe343dc489d4efcc8689270ac44c1ee0e
Transactions (1)
Coinbaseae3fed37442a19…9270ac44c1ee0e
1 in β†’ 2 out8.8600 XPM152 B
AJgZBh3x…9DpUcwi5ALPu3s2c…EJXLjVFh
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.

2.051 Γ— 10⁹⁷(98-digit number)
20517483225872488834…75161268996181043200
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
2.051 Γ— 10⁹⁷(98-digit number)
20517483225872488834…75161268996181043201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.103 Γ— 10⁹⁷(98-digit number)
41034966451744977669…50322537992362086401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.206 Γ— 10⁹⁷(98-digit number)
82069932903489955338…00645075984724172801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.641 Γ— 10⁹⁸(99-digit number)
16413986580697991067…01290151969448345601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.282 Γ— 10⁹⁸(99-digit number)
32827973161395982135…02580303938896691201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.565 Γ— 10⁹⁸(99-digit number)
65655946322791964270…05160607877793382401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.313 Γ— 10⁹⁹(100-digit number)
13131189264558392854…10321215755586764801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.626 Γ— 10⁹⁹(100-digit number)
26262378529116785708…20642431511173529601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.252 Γ— 10⁹⁹(100-digit number)
52524757058233571416…41284863022347059201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.050 Γ— 10¹⁰⁰(101-digit number)
10504951411646714283…82569726044694118401
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 1534675

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 ecc5146684873155c4dfd5d67423bad6c20dd3b672ebe7d7a1a4eb21cb2241fc

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 #1,534,675 on Chainz β†—
Circulating Supply:57,762,948 XPMΒ·at block #6,814,857 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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