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Block #34,473

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 6:33:48 AM Β· Difficulty 7.9933 Β· 6,775,701 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
93c0eccdcf3a53ef2d2e2ae54361f9bfed89aee1df9523a7bcadb7e8f14f0ee0
View on Chainz β†—

Height

#34,473

Difficulty

7.993329

Transactions

1

Size

200 B

Version

2

Bits

07fe4acd

Nonce

0

Timestamp

7/14/2013, 6:33:48 AM

Confirmations

6,775,701

Merkle Root

d69b64ce83f37fb95d7467b31af2648f427d1e6d5872f208b7d0d74a596dad57
Transactions (1)
Coinbased69b64ce83f37f…d0d74a596dad57
1 in β†’ 1 out15.6300 XPM110 B
AXWfKdRc…y1149GUr
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.

3.590 Γ— 10⁹⁴(95-digit number)
35905344948532358126…37325835337135804640
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
3.590 Γ— 10⁹⁴(95-digit number)
35905344948532358126…37325835337135804639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.181 Γ— 10⁹⁴(95-digit number)
71810689897064716252…74651670674271609279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.436 Γ— 10⁹⁡(96-digit number)
14362137979412943250…49303341348543218559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.872 Γ— 10⁹⁡(96-digit number)
28724275958825886500…98606682697086437119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.744 Γ— 10⁹⁡(96-digit number)
57448551917651773001…97213365394172874239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.148 Γ— 10⁹⁢(97-digit number)
11489710383530354600…94426730788345748479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.297 Γ— 10⁹⁢(97-digit number)
22979420767060709200…88853461576691496959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.595 Γ— 10⁹⁢(97-digit number)
45958841534121418401…77706923153382993919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 34473

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 93c0eccdcf3a53ef2d2e2ae54361f9bfed89aee1df9523a7bcadb7e8f14f0ee0

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 #34,473 on Chainz β†—
Circulating Supply:57,725,460 XPMΒ·at block #6,810,173 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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