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Block #61,702

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2013, 2:54:40 PM Β· Difficulty 8.9740 Β· 6,736,229 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1a2a5c76e30a3d954421c120a4d3f802b80254ef315ceec879931dd273c00bb2
View on Chainz β†—

Height

#61,702

Difficulty

8.974014

Transactions

1

Size

198 B

Version

2

Bits

08f958ff

Nonce

515

Timestamp

7/18/2013, 2:54:40 PM

Confirmations

6,736,229

Merkle Root

22b7f279901b0d85d8e9f1a0a47cd46236b011eb7677aa82cdfea5430c822c85
Transactions (1)
Coinbase22b7f279901b0d…fea5430c822c85
1 in β†’ 1 out12.4000 XPM110 B
AHDegLfg…2QdrgJ8J
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.

7.816 Γ— 10⁸⁸(89-digit number)
78166839926679239094…50112463967937686500
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
7.816 Γ— 10⁸⁸(89-digit number)
78166839926679239094…50112463967937686501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.563 Γ— 10⁸⁹(90-digit number)
15633367985335847818…00224927935875373001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.126 Γ— 10⁸⁹(90-digit number)
31266735970671695637…00449855871750746001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.253 Γ— 10⁸⁹(90-digit number)
62533471941343391275…00899711743501492001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.250 Γ— 10⁹⁰(91-digit number)
12506694388268678255…01799423487002984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.501 Γ— 10⁹⁰(91-digit number)
25013388776537356510…03598846974005968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.002 Γ— 10⁹⁰(91-digit number)
50026777553074713020…07197693948011936001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.000 Γ— 10⁹¹(92-digit number)
10005355510614942604…14395387896023872001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.001 Γ— 10⁹¹(92-digit number)
20010711021229885208…28790775792047744001
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 61702

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 1a2a5c76e30a3d954421c120a4d3f802b80254ef315ceec879931dd273c00bb2

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 #61,702 on Chainz β†—
Circulating Supply:57,627,438 XPMΒ·at block #6,797,930 Β· updates every 60s
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