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Block #617,920

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/5/2014, 9:09:15 AM Β· Difficulty 10.9466 Β· 6,208,620 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
16e824403f1ebd9b204af8f55ad654900258af4907492d80a7ba355356b4d7f2
View on Chainz β†—

Height

#617,920

Difficulty

10.946604

Transactions

1

Size

206 B

Version

2

Bits

0af254ab

Nonce

1,680,432,869

Timestamp

7/5/2014, 9:09:15 AM

Confirmations

6,208,620

Merkle Root

96a393da4e145bd4d9a856384d1ce0c2e1598ae67f7c7b3b0b4f17b33f2e0f9c
Transactions (1)
Coinbase96a393da4e145b…4f17b33f2e0f9c
1 in β†’ 1 out8.3300 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.

7.790 Γ— 10⁹⁴(95-digit number)
77906015042186885875…55097849374733084000
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
7.790 Γ— 10⁹⁴(95-digit number)
77906015042186885875…55097849374733083999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.558 Γ— 10⁹⁡(96-digit number)
15581203008437377175…10195698749466167999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.116 Γ— 10⁹⁡(96-digit number)
31162406016874754350…20391397498932335999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.232 Γ— 10⁹⁡(96-digit number)
62324812033749508700…40782794997864671999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.246 Γ— 10⁹⁢(97-digit number)
12464962406749901740…81565589995729343999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.492 Γ— 10⁹⁢(97-digit number)
24929924813499803480…63131179991458687999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.985 Γ— 10⁹⁢(97-digit number)
49859849626999606960…26262359982917375999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.971 Γ— 10⁹⁢(97-digit number)
99719699253999213920…52524719965834751999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.994 Γ— 10⁹⁷(98-digit number)
19943939850799842784…05049439931669503999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.988 Γ— 10⁹⁷(98-digit number)
39887879701599685568…10098879863339007999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.977 Γ— 10⁹⁷(98-digit number)
79775759403199371136…20197759726678015999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 617920

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 16e824403f1ebd9b204af8f55ad654900258af4907492d80a7ba355356b4d7f2

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 #617,920 on Chainz β†—
Circulating Supply:57,856,468 XPMΒ·at block #6,826,539 Β· updates every 60s
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