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Block #88,490

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/29/2013, 4:14:02 PM Β· Difficulty 9.2671 Β· 6,709,311 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
efd8b64ecab2344fd21804ed106463c9a0847618948d4815463a6190253d0576
View on Chainz β†—

Height

#88,490

Difficulty

9.267125

Transactions

2

Size

721 B

Version

2

Bits

0944624b

Nonce

62,510

Timestamp

7/29/2013, 4:14:02 PM

Confirmations

6,709,311

Merkle Root

bca944c2719ed97473805d239681a6b26a7be4e3c025f26c954e5193dba86b1d
Transactions (2)
Coinbase71a02c718d052e…56b783c8b2d891
1 in β†’ 1 out11.6400 XPM109 B
AWuDuxGX…tLDpHWp7
4b9e0806e493ae…80170b4997ec60
3 in β†’ 2 out0.1176 XPM521 B
AUBWFp6t…k781MHB8AaQSR66X…gZM72dnk
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.

1.175 Γ— 10⁹⁢(97-digit number)
11756597672598594299…07991029137374121690
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
1.175 Γ— 10⁹⁢(97-digit number)
11756597672598594299…07991029137374121691
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.351 Γ— 10⁹⁢(97-digit number)
23513195345197188599…15982058274748243381
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.702 Γ— 10⁹⁢(97-digit number)
47026390690394377198…31964116549496486761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.405 Γ— 10⁹⁢(97-digit number)
94052781380788754397…63928233098992973521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.881 Γ— 10⁹⁷(98-digit number)
18810556276157750879…27856466197985947041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.762 Γ— 10⁹⁷(98-digit number)
37621112552315501759…55712932395971894081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.524 Γ— 10⁹⁷(98-digit number)
75242225104631003518…11425864791943788161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.504 Γ— 10⁹⁸(99-digit number)
15048445020926200703…22851729583887576321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.009 Γ— 10⁹⁸(99-digit number)
30096890041852401407…45703459167775152641
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 88490

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 efd8b64ecab2344fd21804ed106463c9a0847618948d4815463a6190253d0576

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 #88,490 on Chainz β†—
Circulating Supply:57,626,384 XPMΒ·at block #6,797,800 Β· updates every 60s
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