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Block #115,502

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/13/2013, 7:42:37 PM Β· Difficulty 9.7446 Β· 6,696,251 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
86117245de1f532fa12d03479d19e191b8172488166110df1083afd5913e007d
View on Chainz β†—

Height

#115,502

Difficulty

9.744581

Transactions

1

Size

207 B

Version

2

Bits

09be9ce2

Nonce

147,369

Timestamp

8/13/2013, 7:42:37 PM

Confirmations

6,696,251

Merkle Root

d81065c69c878b1c93dce5e79649146f386d308a48f7a7984723fad017e2ca9f
Transactions (1)
Coinbased81065c69c878b…23fad017e2ca9f
1 in β†’ 1 out10.5200 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.

2.132 Γ— 10¹⁰⁷(108-digit number)
21329009578911506866…70742331310858364600
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
2.132 Γ— 10¹⁰⁷(108-digit number)
21329009578911506866…70742331310858364599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.265 Γ— 10¹⁰⁷(108-digit number)
42658019157823013733…41484662621716729199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.531 Γ— 10¹⁰⁷(108-digit number)
85316038315646027467…82969325243433458399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.706 Γ— 10¹⁰⁸(109-digit number)
17063207663129205493…65938650486866916799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.412 Γ— 10¹⁰⁸(109-digit number)
34126415326258410987…31877300973733833599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.825 Γ— 10¹⁰⁸(109-digit number)
68252830652516821974…63754601947467667199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.365 Γ— 10¹⁰⁹(110-digit number)
13650566130503364394…27509203894935334399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.730 Γ— 10¹⁰⁹(110-digit number)
27301132261006728789…55018407789870668799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.460 Γ— 10¹⁰⁹(110-digit number)
54602264522013457579…10036815579741337599
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 115502

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 86117245de1f532fa12d03479d19e191b8172488166110df1083afd5913e007d

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 #115,502 on Chainz β†—
Circulating Supply:57,738,133 XPMΒ·at block #6,811,752 Β· updates every 60s
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