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Block #137,425

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/27/2013, 7:25:20 PM Β· Difficulty 9.8215 Β· 6,675,262 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fcafccdd8f4b666d49a5c56dac50d81c28b68a9a89305f35dcca87909353bbae
View on Chainz β†—

Height

#137,425

Difficulty

9.821455

Transactions

1

Size

198 B

Version

2

Bits

09d24ada

Nonce

221,054

Timestamp

8/27/2013, 7:25:20 PM

Confirmations

6,675,262

Merkle Root

c17d02b2bad55dcde650ddcb384b3ac8a09ebb4518991ed7baa86eefaec64751
Transactions (1)
Coinbasec17d02b2bad55d…a86eefaec64751
1 in β†’ 1 out10.3500 XPM109 B
AG9ocqwr…2MwsAk9z
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.

2.031 Γ— 10⁹²(93-digit number)
20319941430297512231…76279224210408710080
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
2.031 Γ— 10⁹²(93-digit number)
20319941430297512231…76279224210408710081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.063 Γ— 10⁹²(93-digit number)
40639882860595024463…52558448420817420161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.127 Γ— 10⁹²(93-digit number)
81279765721190048926…05116896841634840321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.625 Γ— 10⁹³(94-digit number)
16255953144238009785…10233793683269680641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.251 Γ— 10⁹³(94-digit number)
32511906288476019570…20467587366539361281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.502 Γ— 10⁹³(94-digit number)
65023812576952039141…40935174733078722561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.300 Γ— 10⁹⁴(95-digit number)
13004762515390407828…81870349466157445121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.600 Γ— 10⁹⁴(95-digit number)
26009525030780815656…63740698932314890241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.201 Γ— 10⁹⁴(95-digit number)
52019050061561631313…27481397864629780481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.040 Γ— 10⁹⁡(96-digit number)
10403810012312326262…54962795729259560961
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 137425

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 fcafccdd8f4b666d49a5c56dac50d81c28b68a9a89305f35dcca87909353bbae

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 #137,425 on Chainz β†—
Circulating Supply:57,745,530 XPMΒ·at block #6,812,686 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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