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Block #104,537

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2013, 2:32:27 AM Β· Difficulty 9.5597 Β· 6,721,156 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9fc8e0c61186b3759d569c0ff2d60419c6f4aa18dc722f4c934661fc04ee5438
View on Chainz β†—

Height

#104,537

Difficulty

9.559745

Transactions

2

Size

1019 B

Version

2

Bits

098f4b71

Nonce

30,225

Timestamp

8/8/2013, 2:32:27 AM

Confirmations

6,721,156

Merkle Root

5e29791b268b066b189039280bbce6a869faab5c812b15bbdeb00797258117c5
Transactions (2)
Coinbasebed40ac3da6771…c5bfb376eaf0f9
1 in β†’ 1 out10.9500 XPM109 B
AeUkFPH5…2jXKyhKW
dc46d1aad78eb6…d44292ad8262d2
5 in β†’ 2 out2.0430 XPM819 B
AR8bqJWK…dLQMZRhWAPsLvJF1…md6KNwCs
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.

1.280 Γ— 10⁹⁸(99-digit number)
12808746316759720945…91873037298038428280
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
1.280 Γ— 10⁹⁸(99-digit number)
12808746316759720945…91873037298038428279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.561 Γ— 10⁹⁸(99-digit number)
25617492633519441890…83746074596076856559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.123 Γ— 10⁹⁸(99-digit number)
51234985267038883780…67492149192153713119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.024 Γ— 10⁹⁹(100-digit number)
10246997053407776756…34984298384307426239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.049 Γ— 10⁹⁹(100-digit number)
20493994106815553512…69968596768614852479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.098 Γ— 10⁹⁹(100-digit number)
40987988213631107024…39937193537229704959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.197 Γ— 10⁹⁹(100-digit number)
81975976427262214049…79874387074459409919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.639 Γ— 10¹⁰⁰(101-digit number)
16395195285452442809…59748774148918819839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.279 Γ— 10¹⁰⁰(101-digit number)
32790390570904885619…19497548297837639679
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 104537

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 9fc8e0c61186b3759d569c0ff2d60419c6f4aa18dc722f4c934661fc04ee5438

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 #104,537 on Chainz β†—
Circulating Supply:57,849,656 XPMΒ·at block #6,825,692 Β· updates every 60s
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