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Block #135,477

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/26/2013, 3:49:40 PM Β· Difficulty 9.8107 Β· 6,690,637 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a2e92abde56760b4e185fdadf83ace1c0ab4a026e1172a1c754d7f03ee2c99a3
View on Chainz β†—

Height

#135,477

Difficulty

9.810682

Transactions

1

Size

200 B

Version

2

Bits

09cf88e3

Nonce

118,689

Timestamp

8/26/2013, 3:49:40 PM

Confirmations

6,690,637

Merkle Root

e8843d382aba70b3924046a36b13ee25d5db2644dde307c49d0efc8ce197cc8e
Transactions (1)
Coinbasee8843d382aba70…0efc8ce197cc8e
1 in β†’ 1 out10.3700 XPM109 B
AbGZum2d…44MDDShz
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.

2.897 Γ— 10⁹⁢(97-digit number)
28974464858334639626…34191893914960465040
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
2.897 Γ— 10⁹⁢(97-digit number)
28974464858334639626…34191893914960465041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.794 Γ— 10⁹⁢(97-digit number)
57948929716669279252…68383787829920930081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.158 Γ— 10⁹⁷(98-digit number)
11589785943333855850…36767575659841860161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.317 Γ— 10⁹⁷(98-digit number)
23179571886667711701…73535151319683720321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.635 Γ— 10⁹⁷(98-digit number)
46359143773335423402…47070302639367440641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.271 Γ— 10⁹⁷(98-digit number)
92718287546670846804…94140605278734881281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.854 Γ— 10⁹⁸(99-digit number)
18543657509334169360…88281210557469762561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.708 Γ— 10⁹⁸(99-digit number)
37087315018668338721…76562421114939525121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.417 Γ— 10⁹⁸(99-digit number)
74174630037336677443…53124842229879050241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.483 Γ— 10⁹⁹(100-digit number)
14834926007467335488…06249684459758100481
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 135477

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 a2e92abde56760b4e185fdadf83ace1c0ab4a026e1172a1c754d7f03ee2c99a3

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 #135,477 on Chainz β†—
Circulating Supply:57,853,037 XPMΒ·at block #6,826,113 Β· updates every 60s
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