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Home/Chain Registry/Block #1,985,052

Block #1,985,052

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/16/2017, 12:15:24 AM Β· Difficulty 10.7420 Β· 4,856,211 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f95df97ef99e3cdd206205f9ef7cda6140ee56752a08f5c22698c0c1aecb8670
View on Chainz β†—

Difficulty

10.742027

Transactions

1

Size

243 B

Version

2

Bits

0abdf57b

Nonce

416,501,355

Timestamp

2/16/2017, 12:15:24 AM

Confirmations

4,856,211

Merkle Root

3571d12e6a2c345c2438b0f5afe64cb3ae612f6dfb8363c6152d0b970b32b8fa
Transactions (1)
Coinbase3571d12e6a2c34…2d0b970b32b8fa
1 in β†’ 2 out8.6500 XPM152 B
AYK1QFZ4…PR5iJU9QALPu3s2c…EJXLjVFh
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.

1.821 Γ— 10⁹⁢(97-digit number)
18216806855944853476…39139394225880366080
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
1.821 Γ— 10⁹⁢(97-digit number)
18216806855944853476…39139394225880366081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.643 Γ— 10⁹⁢(97-digit number)
36433613711889706952…78278788451760732161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.286 Γ— 10⁹⁢(97-digit number)
72867227423779413905…56557576903521464321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.457 Γ— 10⁹⁷(98-digit number)
14573445484755882781…13115153807042928641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.914 Γ— 10⁹⁷(98-digit number)
29146890969511765562…26230307614085857281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.829 Γ— 10⁹⁷(98-digit number)
58293781939023531124…52460615228171714561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.165 Γ— 10⁹⁸(99-digit number)
11658756387804706224…04921230456343429121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.331 Γ— 10⁹⁸(99-digit number)
23317512775609412449…09842460912686858241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.663 Γ— 10⁹⁸(99-digit number)
46635025551218824899…19684921825373716481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.327 Γ— 10⁹⁸(99-digit number)
93270051102437649799…39369843650747432961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1985052

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 f95df97ef99e3cdd206205f9ef7cda6140ee56752a08f5c22698c0c1aecb8670

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 #1,985,052 on Chainz β†—
Circulating Supply:57,974,468 XPMΒ·at block #6,841,262 Β· updates every 60s
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