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Block #2,676,547

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/24/2018, 11:00:21 PM Β· Difficulty 11.6976 Β· 4,167,097 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
212c6f8429926cfe01a2dad4f16d569eeb59537f5f182cc46a50a4364c0ac40f
View on Chainz β†—

Difficulty

11.697616

Transactions

1

Size

201 B

Version

2

Bits

0bb296f5

Nonce

739,052,251

Timestamp

5/24/2018, 11:00:21 PM

Confirmations

4,167,097

Merkle Root

1b1af92a64806204ea1bd08b003ec93e14a299818c7d5d9895a25bdcdc5f8a0e
Transactions (1)
Coinbase1b1af92a648062…a25bdcdc5f8a0e
1 in β†’ 1 out7.3000 XPM110 B
AeLaaab6…CH7aNdh3
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.

3.889 Γ— 10⁹⁢(97-digit number)
38891871197387562172…43110311819759759360
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
3.889 Γ— 10⁹⁢(97-digit number)
38891871197387562172…43110311819759759361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.778 Γ— 10⁹⁢(97-digit number)
77783742394775124345…86220623639519518721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.555 Γ— 10⁹⁷(98-digit number)
15556748478955024869…72441247279039037441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.111 Γ— 10⁹⁷(98-digit number)
31113496957910049738…44882494558078074881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.222 Γ— 10⁹⁷(98-digit number)
62226993915820099476…89764989116156149761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.244 Γ— 10⁹⁸(99-digit number)
12445398783164019895…79529978232312299521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.489 Γ— 10⁹⁸(99-digit number)
24890797566328039790…59059956464624599041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.978 Γ— 10⁹⁸(99-digit number)
49781595132656079581…18119912929249198081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.956 Γ— 10⁹⁸(99-digit number)
99563190265312159162…36239825858498396161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.991 Γ— 10⁹⁹(100-digit number)
19912638053062431832…72479651716996792321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.982 Γ— 10⁹⁹(100-digit number)
39825276106124863665…44959303433993584641
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 2676547

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 212c6f8429926cfe01a2dad4f16d569eeb59537f5f182cc46a50a4364c0ac40f

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 #2,676,547 on Chainz β†—
Circulating Supply:57,993,522 XPMΒ·at block #6,843,643 Β· updates every 60s
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