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Block #1,064,056

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/18/2015, 12:24:49 AM Β· Difficulty 10.7297 Β· 5,781,286 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
adab76d9c2c9a3706fa9bc3cb47f88a9981211d9bc4b0a3b326b049a8c6ee2ce
View on Chainz β†—

Height

#1,064,056

Difficulty

10.729670

Transactions

2

Size

3.32 KB

Version

2

Bits

0abacbaf

Nonce

2,996,822,843

Timestamp

5/18/2015, 12:24:49 AM

Confirmations

5,781,286

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7ec90a9419c6259f4e064ddf558f96bf1a97f1c349f02b92af20c9e116f56d4d
Transactions (2)
Coinbased93457b068e7c2…f53bb36b4e0967
1 in β†’ 1 out8.7500 XPM116 B
ANSXnLY2…Sd25TjkD
e3071939d65a33…1c1dcb7c5ef60a
21 in β†’ 2 out1416.8333 XPM3.11 KB
Ac7TmQJ3…F6w332YrAHJiHDyn…LQjujK34
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.

2.143 Γ— 10⁹⁢(97-digit number)
21433590919519645219…35942131296977755521
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
2.143 Γ— 10⁹⁢(97-digit number)
21433590919519645219…35942131296977755521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.286 Γ— 10⁹⁢(97-digit number)
42867181839039290438…71884262593955511041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.573 Γ— 10⁹⁢(97-digit number)
85734363678078580877…43768525187911022081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.714 Γ— 10⁹⁷(98-digit number)
17146872735615716175…87537050375822044161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.429 Γ— 10⁹⁷(98-digit number)
34293745471231432351…75074100751644088321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.858 Γ— 10⁹⁷(98-digit number)
68587490942462864702…50148201503288176641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.371 Γ— 10⁹⁸(99-digit number)
13717498188492572940…00296403006576353281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.743 Γ— 10⁹⁸(99-digit number)
27434996376985145880…00592806013152706561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.486 Γ— 10⁹⁸(99-digit number)
54869992753970291761…01185612026305413121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.097 Γ— 10⁹⁹(100-digit number)
10973998550794058352…02371224052610826241
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:58,007,177 XPMΒ·at block #6,845,341 Β· updates every 60s
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