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Block #103,122

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2013, 10:57:17 AM Β· Difficulty 9.5158 Β· 6,692,332 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8bdbfe9dd4dbf08211d933883f0121950ec030d3cfd4c459085e9d8812a8d408
View on Chainz β†—

Height

#103,122

Difficulty

9.515790

Transactions

1

Size

201 B

Version

2

Bits

09840ad8

Nonce

283,305

Timestamp

8/7/2013, 10:57:17 AM

Confirmations

6,692,332

Merkle Root

a2179a771df33c1539032333c7789834290d3d533c9d455742401a3e31ce47bd
Transactions (1)
Coinbasea2179a771df33c…401a3e31ce47bd
1 in β†’ 1 out11.0300 XPM109 B
Abn1QADX…XZwY8A9C
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.

1.006 Γ— 10¹⁰⁰(101-digit number)
10061420627112645038…34012122509492948430
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
1.006 Γ— 10¹⁰⁰(101-digit number)
10061420627112645038…34012122509492948431
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.012 Γ— 10¹⁰⁰(101-digit number)
20122841254225290077…68024245018985896861
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.024 Γ— 10¹⁰⁰(101-digit number)
40245682508450580154…36048490037971793721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.049 Γ— 10¹⁰⁰(101-digit number)
80491365016901160308…72096980075943587441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.609 Γ— 10¹⁰¹(102-digit number)
16098273003380232061…44193960151887174881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.219 Γ— 10¹⁰¹(102-digit number)
32196546006760464123…88387920303774349761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.439 Γ— 10¹⁰¹(102-digit number)
64393092013520928247…76775840607548699521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.287 Γ— 10¹⁰²(103-digit number)
12878618402704185649…53551681215097399041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.575 Γ— 10¹⁰²(103-digit number)
25757236805408371298…07103362430194798081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.151 Γ— 10¹⁰²(103-digit number)
51514473610816742597…14206724860389596161
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 103122

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 8bdbfe9dd4dbf08211d933883f0121950ec030d3cfd4c459085e9d8812a8d408

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 #103,122 on Chainz β†—
Circulating Supply:57,607,691 XPMΒ·at block #6,795,453 Β· updates every 60s
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