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Block #86,147

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/27/2013, 10:25:31 PM Β· Difficulty 9.2905 Β· 6,708,567 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c08d77486d74d74a7b3382f7af78ca6b18d60d6f3403cff63c94fb0fa8a688c1
View on Chainz β†—

Height

#86,147

Difficulty

9.290486

Transactions

1

Size

202 B

Version

2

Bits

094a5d44

Nonce

41,031

Timestamp

7/27/2013, 10:25:31 PM

Confirmations

6,708,567

Merkle Root

dd9f305741c5701ca4fed4f7d793c2855ae4afe15f27905fef108ea4b2c0b81a
Transactions (1)
Coinbasedd9f305741c570…108ea4b2c0b81a
1 in β†’ 1 out11.5700 XPM109 B
ASXW8s4r…LM8vqY9U
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.

2.594 Γ— 10¹⁰¹(102-digit number)
25941050429602582418…10437675106845291800
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.594 Γ— 10¹⁰¹(102-digit number)
25941050429602582418…10437675106845291799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.188 Γ— 10¹⁰¹(102-digit number)
51882100859205164837…20875350213690583599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.037 Γ— 10¹⁰²(103-digit number)
10376420171841032967…41750700427381167199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.075 Γ— 10¹⁰²(103-digit number)
20752840343682065934…83501400854762334399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.150 Γ— 10¹⁰²(103-digit number)
41505680687364131869…67002801709524668799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.301 Γ— 10¹⁰²(103-digit number)
83011361374728263739…34005603419049337599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.660 Γ— 10¹⁰³(104-digit number)
16602272274945652747…68011206838098675199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.320 Γ— 10¹⁰³(104-digit number)
33204544549891305495…36022413676197350399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.640 Γ— 10¹⁰³(104-digit number)
66409089099782610991…72044827352394700799
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 86147

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 c08d77486d74d74a7b3382f7af78ca6b18d60d6f3403cff63c94fb0fa8a688c1

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 #86,147 on Chainz β†—
Circulating Supply:57,601,760 XPMΒ·at block #6,794,713 Β· updates every 60s
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