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Block #53,765

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2013, 4:54:56 PM Β· Difficulty 8.9270 Β· 6,742,240 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
938d23f14d925641ffb13f5af8210f759e3c3046c6ab73227c06f9a65c29a44a
View on Chainz β†—

Height

#53,765

Difficulty

8.926991

Transactions

1

Size

198 B

Version

2

Bits

08ed4f41

Nonce

174

Timestamp

7/16/2013, 4:54:56 PM

Confirmations

6,742,240

Mined by

⛏️ P2SHAMEZhQcJCYXJaqsM8aDBT7TXZLS4v3jrb8

Merkle Root

a6e34447299c4c4849c5214630dd03b24c2f676b28da6a9bfe9cc076a25b8d52
Transactions (1)
Coinbasea6e34447299c4c…9cc076a25b8d52
1 in β†’ 1 out12.5300 XPM110 B
AMEZhQcJ…S4v3jrb8
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.

2.384 Γ— 10⁹⁰(91-digit number)
23841105694898293445…38285361554558672161
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
2.384 Γ— 10⁹⁰(91-digit number)
23841105694898293445…38285361554558672161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.768 Γ— 10⁹⁰(91-digit number)
47682211389796586890…76570723109117344321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.536 Γ— 10⁹⁰(91-digit number)
95364422779593173780…53141446218234688641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.907 Γ— 10⁹¹(92-digit number)
19072884555918634756…06282892436469377281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.814 Γ— 10⁹¹(92-digit number)
38145769111837269512…12565784872938754561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.629 Γ— 10⁹¹(92-digit number)
76291538223674539024…25131569745877509121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.525 Γ— 10⁹²(93-digit number)
15258307644734907804…50263139491755018241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.051 Γ— 10⁹²(93-digit number)
30516615289469815609…00526278983510036481
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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, …
Cross-reference on Chainz Explorer
Circulating Supply:57,612,129 XPMΒ·at block #6,796,004 Β· updates every 60s
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