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Home/Chain Registry/Block #2,135,742

Block #2,135,742

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/28/2017, 12:36:13 PM Β· Difficulty 10.8987 Β· 4,705,201 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
acc84f973c34bb46667fd91c8dce4890d7a13463b1a59124ac855659378595df
View on Chainz β†—

Difficulty

10.898713

Transactions

1

Size

199 B

Version

2

Bits

0ae61209

Nonce

1,206,691,176

Timestamp

5/28/2017, 12:36:13 PM

Confirmations

4,705,201

Merkle Root

d67017269f74d9743aefc30b4eff8e85c6b6e747817715fba9ee4b17334a9866
Transactions (1)
Coinbased67017269f74d9…ee4b17334a9866
1 in β†’ 1 out8.4100 XPM109 B
ATpBjVa6…FJ3pFFq7
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.

9.999 Γ— 10⁹³(94-digit number)
99998584247220939644…00765623850008691200
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
9.999 Γ— 10⁹³(94-digit number)
99998584247220939644…00765623850008691201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.999 Γ— 10⁹⁴(95-digit number)
19999716849444187928…01531247700017382401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.999 Γ— 10⁹⁴(95-digit number)
39999433698888375857…03062495400034764801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.999 Γ— 10⁹⁴(95-digit number)
79998867397776751715…06124990800069529601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.599 Γ— 10⁹⁡(96-digit number)
15999773479555350343…12249981600139059201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.199 Γ— 10⁹⁡(96-digit number)
31999546959110700686…24499963200278118401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.399 Γ— 10⁹⁡(96-digit number)
63999093918221401372…48999926400556236801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.279 Γ— 10⁹⁢(97-digit number)
12799818783644280274…97999852801112473601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.559 Γ— 10⁹⁢(97-digit number)
25599637567288560548…95999705602224947201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.119 Γ— 10⁹⁢(97-digit number)
51199275134577121097…91999411204449894401
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 2135742

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 acc84f973c34bb46667fd91c8dce4890d7a13463b1a59124ac855659378595df

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 #2,135,742 on Chainz β†—
Circulating Supply:57,971,897 XPMΒ·at block #6,840,942 Β· updates every 60s
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