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Block #70,552

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2013, 2:10:48 PM Β· Difficulty 8.9923 Β· 6,756,139 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3778ed737fab4a1704995968bcce68d2b2ff6460a535024fac8502c76a3e6f72
View on Chainz β†—

Height

#70,552

Difficulty

8.992281

Transactions

1

Size

204 B

Version

2

Bits

08fe061a

Nonce

838

Timestamp

7/20/2013, 2:10:48 PM

Confirmations

6,756,139

Merkle Root

d37d088e1a0c0d087f860240eaba67080b7b859522c5b8f8d843c0ed9ed2e520
Transactions (1)
Coinbased37d088e1a0c0d…43c0ed9ed2e520
1 in β†’ 1 out12.3500 XPM110 B
APZw681P…Yv3wDWd9
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.

1.269 Γ— 10¹⁰⁡(106-digit number)
12692629823594110673…67780868710194630000
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
1.269 Γ— 10¹⁰⁡(106-digit number)
12692629823594110673…67780868710194630001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.538 Γ— 10¹⁰⁡(106-digit number)
25385259647188221346…35561737420389260001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.077 Γ— 10¹⁰⁡(106-digit number)
50770519294376442693…71123474840778520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.015 Γ— 10¹⁰⁢(107-digit number)
10154103858875288538…42246949681557040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.030 Γ— 10¹⁰⁢(107-digit number)
20308207717750577077…84493899363114080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.061 Γ— 10¹⁰⁢(107-digit number)
40616415435501154155…68987798726228160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.123 Γ— 10¹⁰⁢(107-digit number)
81232830871002308310…37975597452456320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.624 Γ— 10¹⁰⁷(108-digit number)
16246566174200461662…75951194904912640001
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 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 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 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 70552

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 3778ed737fab4a1704995968bcce68d2b2ff6460a535024fac8502c76a3e6f72

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 #70,552 on Chainz β†—
Circulating Supply:57,857,679 XPMΒ·at block #6,826,690 Β· updates every 60s
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