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Block #139,515

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/29/2013, 1:23:31 AM Β· Difficulty 9.8316 Β· 6,678,415 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
798cce274beee3afb63c4091de6fabbb8a53e680e482ab61e2a193d814ccabb2
View on Chainz β†—

Height

#139,515

Difficulty

9.831556

Transactions

1

Size

199 B

Version

2

Bits

09d4e0e0

Nonce

97,883

Timestamp

8/29/2013, 1:23:31 AM

Confirmations

6,678,415

Merkle Root

7aed704d7d58f6def6fc363832fb5e0b0f9010a600e1b03a068c91824f988c47
Transactions (1)
Coinbase7aed704d7d58f6…8c91824f988c47
1 in β†’ 1 out10.3300 XPM109 B
ALJ24E54…CM192Nmg
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.

2.397 Γ— 10⁹³(94-digit number)
23971104571016702499…07011857840627009280
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
2.397 Γ— 10⁹³(94-digit number)
23971104571016702499…07011857840627009281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.794 Γ— 10⁹³(94-digit number)
47942209142033404998…14023715681254018561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.588 Γ— 10⁹³(94-digit number)
95884418284066809996…28047431362508037121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.917 Γ— 10⁹⁴(95-digit number)
19176883656813361999…56094862725016074241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.835 Γ— 10⁹⁴(95-digit number)
38353767313626723998…12189725450032148481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.670 Γ— 10⁹⁴(95-digit number)
76707534627253447996…24379450900064296961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.534 Γ— 10⁹⁡(96-digit number)
15341506925450689599…48758901800128593921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.068 Γ— 10⁹⁡(96-digit number)
30683013850901379198…97517803600257187841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.136 Γ— 10⁹⁡(96-digit number)
61366027701802758397…95035607200514375681
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 139515

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 798cce274beee3afb63c4091de6fabbb8a53e680e482ab61e2a193d814ccabb2

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 #139,515 on Chainz β†—
Circulating Supply:57,787,507 XPMΒ·at block #6,817,929 Β· updates every 60s
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