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Home/Chain Registry/Block #2,859,178

Block #2,859,178

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/29/2018, 2:26:20 AM Β· Difficulty 11.6755 Β· 3,977,807 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
270463062a653685a7740c142bdba3ef75c66c840dd18f5e115f67cc5d56b3c4
View on Chainz β†—

Difficulty

11.675518

Transactions

1

Size

200 B

Version

2

Bits

0baceebf

Nonce

80,810,893

Timestamp

9/29/2018, 2:26:20 AM

Confirmations

3,977,807

Merkle Root

f30d6c425f64c83c538e46ab5c87b15437c8973d9b2256da05796d796a85d7cf
Transactions (1)
Coinbasef30d6c425f64c8…796d796a85d7cf
1 in β†’ 1 out7.3200 XPM110 B
AK7NP1Hs…rrBmoJK1
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.

4.678 Γ— 10⁹⁡(96-digit number)
46785951069562664635…14989517852638277120
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
4.678 Γ— 10⁹⁡(96-digit number)
46785951069562664635…14989517852638277121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.357 Γ— 10⁹⁡(96-digit number)
93571902139125329271…29979035705276554241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.871 Γ— 10⁹⁢(97-digit number)
18714380427825065854…59958071410553108481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.742 Γ— 10⁹⁢(97-digit number)
37428760855650131708…19916142821106216961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.485 Γ— 10⁹⁢(97-digit number)
74857521711300263417…39832285642212433921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.497 Γ— 10⁹⁷(98-digit number)
14971504342260052683…79664571284424867841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.994 Γ— 10⁹⁷(98-digit number)
29943008684520105366…59329142568849735681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.988 Γ— 10⁹⁷(98-digit number)
59886017369040210733…18658285137699471361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.197 Γ— 10⁹⁸(99-digit number)
11977203473808042146…37316570275398942721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.395 Γ— 10⁹⁸(99-digit number)
23954406947616084293…74633140550797885441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.790 Γ— 10⁹⁸(99-digit number)
47908813895232168587…49266281101595770881
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 2859178

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 270463062a653685a7740c142bdba3ef75c66c840dd18f5e115f67cc5d56b3c4

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 #2,859,178 on Chainz β†—
Circulating Supply:57,940,180 XPMΒ·at block #6,836,984 Β· updates every 60s
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