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Home/Chain Registry/Block #2,730,048

Block #2,730,048

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/1/2018, 8:17:37 PM Β· Difficulty 11.6291 Β· 4,102,682 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e0d5953370c289e70a4d1e06db193a0bd12b0fea1390d33e457b9a345605afcc
View on Chainz β†—

Difficulty

11.629128

Transactions

1

Size

200 B

Version

2

Bits

0ba10e90

Nonce

1,079,882,185

Timestamp

7/1/2018, 8:17:37 PM

Confirmations

4,102,682

Merkle Root

ea43c2a33a244010a1f14b857303aade0bd2d2cefc8629077af695dcb5acc3c5
Transactions (1)
Coinbaseea43c2a33a2440…f695dcb5acc3c5
1 in β†’ 1 out7.3800 XPM110 B
AcH8Uiaj…FAbaHZMT
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.

2.972 Γ— 10⁹⁡(96-digit number)
29725276672979243635…66861988478786970240
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
2.972 Γ— 10⁹⁡(96-digit number)
29725276672979243635…66861988478786970241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.945 Γ— 10⁹⁡(96-digit number)
59450553345958487271…33723976957573940481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.189 Γ— 10⁹⁢(97-digit number)
11890110669191697454…67447953915147880961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.378 Γ— 10⁹⁢(97-digit number)
23780221338383394908…34895907830295761921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.756 Γ— 10⁹⁢(97-digit number)
47560442676766789817…69791815660591523841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.512 Γ— 10⁹⁢(97-digit number)
95120885353533579634…39583631321183047681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.902 Γ— 10⁹⁷(98-digit number)
19024177070706715926…79167262642366095361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.804 Γ— 10⁹⁷(98-digit number)
38048354141413431853…58334525284732190721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.609 Γ— 10⁹⁷(98-digit number)
76096708282826863707…16669050569464381441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.521 Γ— 10⁹⁸(99-digit number)
15219341656565372741…33338101138928762881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.043 Γ— 10⁹⁸(99-digit number)
30438683313130745483…66676202277857525761
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 2730048

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 e0d5953370c289e70a4d1e06db193a0bd12b0fea1390d33e457b9a345605afcc

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 #2,730,048 on Chainz β†—
Circulating Supply:57,905,998 XPMΒ·at block #6,832,729 Β· updates every 60s
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