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Block #680,656

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/16/2014, 9:17:59 PM Β· Difficulty 10.9624 Β· 6,120,835 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
27d5f8cf9b2e655cbceb008f4965c7bbb262e9963a3cbaf4fc0c51505c14b0ba
View on Chainz β†—

Height

#680,656

Difficulty

10.962435

Transactions

1

Size

207 B

Version

2

Bits

0af66226

Nonce

163,447,970

Timestamp

8/16/2014, 9:17:59 PM

Confirmations

6,120,835

Merkle Root

33cec5bd710b3e52cd5cb9b2415e6d19b2c7b0f64386d63b3a8271ec1f03e151
Transactions (1)
Coinbase33cec5bd710b3e…8271ec1f03e151
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.759 Γ— 10⁹⁢(97-digit number)
37595687335570782873…76102557859376230400
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
3.759 Γ— 10⁹⁢(97-digit number)
37595687335570782873…76102557859376230401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.519 Γ— 10⁹⁢(97-digit number)
75191374671141565747…52205115718752460801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.503 Γ— 10⁹⁷(98-digit number)
15038274934228313149…04410231437504921601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.007 Γ— 10⁹⁷(98-digit number)
30076549868456626298…08820462875009843201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.015 Γ— 10⁹⁷(98-digit number)
60153099736913252597…17640925750019686401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.203 Γ— 10⁹⁸(99-digit number)
12030619947382650519…35281851500039372801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.406 Γ— 10⁹⁸(99-digit number)
24061239894765301039…70563703000078745601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.812 Γ— 10⁹⁸(99-digit number)
48122479789530602078…41127406000157491201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.624 Γ— 10⁹⁸(99-digit number)
96244959579061204156…82254812000314982401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.924 Γ— 10⁹⁹(100-digit number)
19248991915812240831…64509624000629964801
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 680656

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 27d5f8cf9b2e655cbceb008f4965c7bbb262e9963a3cbaf4fc0c51505c14b0ba

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 #680,656 on Chainz β†—
Circulating Supply:57,655,999 XPMΒ·at block #6,801,490 Β· updates every 60s
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