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Block #88,526

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/29/2013, 4:40:16 PM Β· Difficulty 9.2683 Β· 6,727,747 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2710959decdcbfdb2a7507612fa8919e910554c8c8abfd3ace6f0ee7e6ea413a
View on Chainz β†—

Height

#88,526

Difficulty

9.268325

Transactions

1

Size

207 B

Version

2

Bits

0944b0ed

Nonce

27,501

Timestamp

7/29/2013, 4:40:16 PM

Confirmations

6,727,747

Merkle Root

846fe7879fba51af3d0cf4d64d78a4f3d274a61adba9169eccd60928d76bc8a8
Transactions (1)
Coinbase846fe7879fba51…d60928d76bc8a8
1 in β†’ 1 out11.6200 XPM112 B
AT5A2KL6…CT16n6i2
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.

2.042 Γ— 10¹⁰⁷(108-digit number)
20426946838255905647…78658663266374865260
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
2.042 Γ— 10¹⁰⁷(108-digit number)
20426946838255905647…78658663266374865261
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.085 Γ— 10¹⁰⁷(108-digit number)
40853893676511811294…57317326532749730521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.170 Γ— 10¹⁰⁷(108-digit number)
81707787353023622588…14634653065499461041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.634 Γ— 10¹⁰⁸(109-digit number)
16341557470604724517…29269306130998922081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.268 Γ— 10¹⁰⁸(109-digit number)
32683114941209449035…58538612261997844161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.536 Γ— 10¹⁰⁸(109-digit number)
65366229882418898070…17077224523995688321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.307 Γ— 10¹⁰⁹(110-digit number)
13073245976483779614…34154449047991376641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.614 Γ— 10¹⁰⁹(110-digit number)
26146491952967559228…68308898095982753281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.229 Γ— 10¹⁰⁹(110-digit number)
52292983905935118456…36617796191965506561
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 88526

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 2710959decdcbfdb2a7507612fa8919e910554c8c8abfd3ace6f0ee7e6ea413a

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 #88,526 on Chainz β†—
Circulating Supply:57,774,299 XPMΒ·at block #6,816,272 Β· updates every 60s
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