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Block #159,687

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/11/2013, 8:01:13 AM Β· Difficulty 9.8641 Β· 6,665,623 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cfd7fe942fa90dfecefd25b8463d8faf922ca07b3df2f7788eaf3e77fb568ad9
View on Chainz β†—

Height

#159,687

Difficulty

9.864146

Transactions

1

Size

199 B

Version

2

Bits

09dd38af

Nonce

149,035

Timestamp

9/11/2013, 8:01:13 AM

Confirmations

6,665,623

Merkle Root

49c784d4168777638f09fc20d9ea718b6b4f792dedb939aa6ce8c8b60f5126ad
Transactions (1)
Coinbase49c784d4168777…e8c8b60f5126ad
1 in β†’ 1 out10.2600 XPM109 B
AMjazV56…tVUuP32T
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.

1.036 Γ— 10⁹⁴(95-digit number)
10362900420820020774…19282340583207303400
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
1.036 Γ— 10⁹⁴(95-digit number)
10362900420820020774…19282340583207303401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.072 Γ— 10⁹⁴(95-digit number)
20725800841640041549…38564681166414606801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.145 Γ— 10⁹⁴(95-digit number)
41451601683280083099…77129362332829213601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.290 Γ— 10⁹⁴(95-digit number)
82903203366560166198…54258724665658427201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.658 Γ— 10⁹⁡(96-digit number)
16580640673312033239…08517449331316854401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.316 Γ— 10⁹⁡(96-digit number)
33161281346624066479…17034898662633708801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.632 Γ— 10⁹⁡(96-digit number)
66322562693248132958…34069797325267417601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.326 Γ— 10⁹⁢(97-digit number)
13264512538649626591…68139594650534835201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.652 Γ— 10⁹⁢(97-digit number)
26529025077299253183…36279189301069670401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 159687

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 cfd7fe942fa90dfecefd25b8463d8faf922ca07b3df2f7788eaf3e77fb568ad9

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 #159,687 on Chainz β†—
Circulating Supply:57,846,583 XPMΒ·at block #6,825,309 Β· updates every 60s
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