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Block #1,930,682

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/9/2017, 12:50:46 AM Β· Difficulty 10.7559 Β· 4,907,940 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
881e59b518bb3f851de2c8841966de7ebf4e8a333529348167190703cd80a4ef
View on Chainz β†—

Height

#1,930,682

Difficulty

10.755854

Transactions

2

Size

1.14 KB

Version

2

Bits

0ac17fa1

Nonce

2,001,586,672

Timestamp

1/9/2017, 12:50:46 AM

Confirmations

4,907,940

Mined by

⛏️ P2SHAXRpKLP8CiCewcsU1iMsWg8UAb8V6NpBuB

Merkle Root

93eee57ff4ac573deba282a718a7e03c547629d9b2944a54c557db3e169cf6a9
Transactions (2)
Coinbase1ea9e389ed7a85…fde6b1a1c6195c
1 in β†’ 1 out8.6500 XPM109 B
AXRpKLP8…8V6NpBuB
793ba34b82d1cf…55678f8f40174d
6 in β†’ 2 out9015.6843 XPM968 B
Ada1dx2w…8gd1gZg2AX6oSEZH…DzbktSV7
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.

1.157 Γ— 10⁹³(94-digit number)
11579900140111517529…70340418409124503201
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
1.157 Γ— 10⁹³(94-digit number)
11579900140111517529…70340418409124503201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.315 Γ— 10⁹³(94-digit number)
23159800280223035058…40680836818249006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.631 Γ— 10⁹³(94-digit number)
46319600560446070117…81361673636498012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.263 Γ— 10⁹³(94-digit number)
92639201120892140235…62723347272996025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.852 Γ— 10⁹⁴(95-digit number)
18527840224178428047…25446694545992051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.705 Γ— 10⁹⁴(95-digit number)
37055680448356856094…50893389091984102401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.411 Γ— 10⁹⁴(95-digit number)
74111360896713712188…01786778183968204801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.482 Γ— 10⁹⁡(96-digit number)
14822272179342742437…03573556367936409601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.964 Γ— 10⁹⁡(96-digit number)
29644544358685484875…07147112735872819201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.928 Γ— 10⁹⁡(96-digit number)
59289088717370969750…14294225471745638401
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:57,953,264 XPMΒ·at block #6,838,621 Β· updates every 60s
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