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Block #3,506,247

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/9/2020, 4:47:40 AM Β· Difficulty 10.9304 Β· 3,335,827 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e157ce53cb3103559ccb408afe2e21e0c0619c476e8408cf324172b908b23a22
View on Chainz β†—

Difficulty

10.930399

Transactions

1

Size

201 B

Version

2

Bits

0aee2ea5

Nonce

1,075,618,534

Timestamp

1/9/2020, 4:47:40 AM

Confirmations

3,335,827

Merkle Root

ffa0b22c8175a82875cc20b8a31edef6f57eb588b133bea3e12d020cf3c5cde5
Transactions (1)
Coinbaseffa0b22c8175a8…2d020cf3c5cde5
1 in β†’ 1 out8.3600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

1.508 Γ— 10⁹⁢(97-digit number)
15082621156701339590…25150858795557212160
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
1.508 Γ— 10⁹⁢(97-digit number)
15082621156701339590…25150858795557212161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.016 Γ— 10⁹⁢(97-digit number)
30165242313402679181…50301717591114424321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.033 Γ— 10⁹⁢(97-digit number)
60330484626805358363…00603435182228848641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.206 Γ— 10⁹⁷(98-digit number)
12066096925361071672…01206870364457697281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.413 Γ— 10⁹⁷(98-digit number)
24132193850722143345…02413740728915394561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.826 Γ— 10⁹⁷(98-digit number)
48264387701444286690…04827481457830789121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.652 Γ— 10⁹⁷(98-digit number)
96528775402888573380…09654962915661578241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.930 Γ— 10⁹⁸(99-digit number)
19305755080577714676…19309925831323156481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.861 Γ— 10⁹⁸(99-digit number)
38611510161155429352…38619851662646312961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.722 Γ— 10⁹⁸(99-digit number)
77223020322310858704…77239703325292625921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.544 Γ— 10⁹⁹(100-digit number)
15444604064462171740…54479406650585251841
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 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
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 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 3506247

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 e157ce53cb3103559ccb408afe2e21e0c0619c476e8408cf324172b908b23a22

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 #3,506,247 on Chainz β†—
Circulating Supply:57,980,977 XPMΒ·at block #6,842,073 Β· updates every 60s
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