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Block #655,188

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/30/2014, 5:14:06 PM Β· Difficulty 10.9555 Β· 6,154,255 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6b16be30a43328a933b244dcd8700564b61c2100131c4b5e2108599ae002513b
View on Chainz β†—

Height

#655,188

Difficulty

10.955542

Transactions

1

Size

202 B

Version

2

Bits

0af49e61

Nonce

18,720

Timestamp

7/30/2014, 5:14:06 PM

Confirmations

6,154,255

Mined by

⛏️ P2SHAVUSTGLfXSGYjUDuVVpW48qmaeSeYSsAGR

Merkle Root

dfaa4565752bc82dbf2f92637822436c0cff3d952c2b4eebee1ddb6c0555fb77
Transactions (1)
Coinbasedfaa4565752bc8…1ddb6c0555fb77
1 in β†’ 1 out8.3200 XPM111 B
AVUSTGLf…SeYSsAGR
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.

2.536 Γ— 10⁹⁢(97-digit number)
25360484807609163406…62051699143077804731
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
2.536 Γ— 10⁹⁢(97-digit number)
25360484807609163406…62051699143077804731
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.072 Γ— 10⁹⁢(97-digit number)
50720969615218326812…24103398286155609461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.014 Γ— 10⁹⁷(98-digit number)
10144193923043665362…48206796572311218921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.028 Γ— 10⁹⁷(98-digit number)
20288387846087330724…96413593144622437841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.057 Γ— 10⁹⁷(98-digit number)
40576775692174661449…92827186289244875681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.115 Γ— 10⁹⁷(98-digit number)
81153551384349322899…85654372578489751361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.623 Γ— 10⁹⁸(99-digit number)
16230710276869864579…71308745156979502721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.246 Γ— 10⁹⁸(99-digit number)
32461420553739729159…42617490313959005441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.492 Γ— 10⁹⁸(99-digit number)
64922841107479458319…85234980627918010881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.298 Γ— 10⁹⁹(100-digit number)
12984568221495891663…70469961255836021761
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:57,719,614 XPMΒ·at block #6,809,442 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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