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Block #2,178,410

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/26/2017, 2:21:45 AM Β· Difficulty 10.9261 Β· 4,662,712 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
19dd93cf8dc50e55ee095eb75d3364f23c8022d9e0e62f39a02a8e3b293f760e
View on Chainz β†—

Height

#2,178,410

Difficulty

10.926120

Transactions

1

Size

201 B

Version

2

Bits

0aed1634

Nonce

1,339,070,355

Timestamp

6/26/2017, 2:21:45 AM

Confirmations

4,662,712

Mined by

⛏️ P2SHAeBhM3C8H7SowkRZdZkX1QxxyWQMp14mTw

Merkle Root

f1d816a8bc1c2fa4622606b7d69ee4ed0787015ba160b0a7166d6f4baf249c68
Transactions (1)
Coinbasef1d816a8bc1c2f…6d6f4baf249c68
1 in β†’ 1 out8.3600 XPM110 B
AeBhM3C8…QMp14mTw
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.

3.727 Γ— 10⁹⁢(97-digit number)
37273736662185596152…63858327572017803521
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
3.727 Γ— 10⁹⁢(97-digit number)
37273736662185596152…63858327572017803521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.454 Γ— 10⁹⁢(97-digit number)
74547473324371192304…27716655144035607041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.490 Γ— 10⁹⁷(98-digit number)
14909494664874238460…55433310288071214081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.981 Γ— 10⁹⁷(98-digit number)
29818989329748476921…10866620576142428161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.963 Γ— 10⁹⁷(98-digit number)
59637978659496953843…21733241152284856321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.192 Γ— 10⁹⁸(99-digit number)
11927595731899390768…43466482304569712641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.385 Γ— 10⁹⁸(99-digit number)
23855191463798781537…86932964609139425281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.771 Γ— 10⁹⁸(99-digit number)
47710382927597563074…73865929218278850561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.542 Γ— 10⁹⁸(99-digit number)
95420765855195126149…47731858436557701121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.908 Γ— 10⁹⁹(100-digit number)
19084153171039025229…95463716873115402241
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:57,973,345 XPMΒ·at block #6,841,121 Β· updates every 60s
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