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Block #107,898

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/9/2013, 6:17:59 PM Β· Difficulty 9.6375 Β· 6,688,413 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e0a4b6224a03e7bdb50faf249433fee551284daee9e3d3dfdd0d04484807c0ed
View on Chainz β†—

Height

#107,898

Difficulty

9.637519

Transactions

2

Size

573 B

Version

2

Bits

09a3346a

Nonce

28,259

Timestamp

8/9/2013, 6:17:59 PM

Confirmations

6,688,413

Merkle Root

d93d4483c7a678b3c185cb48661507fcc688143347b24e044361aa701bb75cfc
Transactions (2)
Coinbasef776286e895924…2506f95f1a3f84
1 in β†’ 1 out10.7600 XPM109 B
AVDQbgW4…cziExmpm
bf958b1d02c382…d2d80cb2f15ef3
2 in β†’ 2 out2.0489 XPM372 B
AY7GMWmh…5Khp2HaVAU61evFv…pm8c8Rhf
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.

2.710 Γ— 10⁹⁸(99-digit number)
27108963681105489050…30082132840375092720
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
2.710 Γ— 10⁹⁸(99-digit number)
27108963681105489050…30082132840375092721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.421 Γ— 10⁹⁸(99-digit number)
54217927362210978100…60164265680750185441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.084 Γ— 10⁹⁹(100-digit number)
10843585472442195620…20328531361500370881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.168 Γ— 10⁹⁹(100-digit number)
21687170944884391240…40657062723000741761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.337 Γ— 10⁹⁹(100-digit number)
43374341889768782480…81314125446001483521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.674 Γ— 10⁹⁹(100-digit number)
86748683779537564960…62628250892002967041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.734 Γ— 10¹⁰⁰(101-digit number)
17349736755907512992…25256501784005934081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.469 Γ— 10¹⁰⁰(101-digit number)
34699473511815025984…50513003568011868161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.939 Γ— 10¹⁰⁰(101-digit number)
69398947023630051968…01026007136023736321
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 107898

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 e0a4b6224a03e7bdb50faf249433fee551284daee9e3d3dfdd0d04484807c0ed

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 #107,898 on Chainz β†—
Circulating Supply:57,614,475 XPMΒ·at block #6,796,310 Β· updates every 60s
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