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Block #557,572

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/23/2014, 1:05:11 AM Β· Difficulty 10.9630 Β· 6,237,814 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3b8228664b84d9bbc592c9c28392a5dab61a78fdb8b7a6b9ebd2002ccbe109af
View on Chainz β†—

Height

#557,572

Difficulty

10.962951

Transactions

2

Size

400 B

Version

2

Bits

0af683f4

Nonce

905,829,894

Timestamp

5/23/2014, 1:05:11 AM

Confirmations

6,237,814

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

de4c0b297ef7feb90107c2934eb7b40468526bf04cf120413f80672d8927a1c5
Transactions (2)
Coinbase0895c6ddc1b30d…2f7799f8803bdd
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
40add30c1d6548…c854b83f3f1fa5
1 in β†’ 2 out8.3100 XPM192 B
AeKNrjNj…1NEq95TaAGRJf5c9…j28JnLsV
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.

2.926 Γ— 10⁹⁸(99-digit number)
29265305129708180635…15222916447986536321
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
2.926 Γ— 10⁹⁸(99-digit number)
29265305129708180635…15222916447986536321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.853 Γ— 10⁹⁸(99-digit number)
58530610259416361270…30445832895973072641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.170 Γ— 10⁹⁹(100-digit number)
11706122051883272254…60891665791946145281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.341 Γ— 10⁹⁹(100-digit number)
23412244103766544508…21783331583892290561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.682 Γ— 10⁹⁹(100-digit number)
46824488207533089016…43566663167784581121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.364 Γ— 10⁹⁹(100-digit number)
93648976415066178033…87133326335569162241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.872 Γ— 10¹⁰⁰(101-digit number)
18729795283013235606…74266652671138324481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.745 Γ— 10¹⁰⁰(101-digit number)
37459590566026471213…48533305342276648961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.491 Γ— 10¹⁰⁰(101-digit number)
74919181132052942426…97066610684553297921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.498 Γ— 10¹⁰¹(102-digit number)
14983836226410588485…94133221369106595841
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.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,607,147 XPMΒ·at block #6,795,385 Β· updates every 60s
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