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Block #348,720

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/7/2014, 11:21:16 PM Β· Difficulty 10.2643 Β· 6,487,851 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f2a2942b10e21c72ed8be1684747c68e5fe93bb7f00c01483dbf581a2d557b88
View on Chainz β†—

Height

#348,720

Difficulty

10.264299

Transactions

1

Size

206 B

Version

2

Bits

0a43a914

Nonce

62,891

Timestamp

1/7/2014, 11:21:16 PM

Confirmations

6,487,851

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e6f7650475a92106070d6d71bb7a4e1e2a52d9bc55f47e49518dbf2ff6229ffa
Transactions (1)
Coinbasee6f7650475a921…8dbf2ff6229ffa
1 in β†’ 1 out9.4800 XPM116 B
AbwWkWZt…kawDhufa
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.

8.774 Γ— 10⁹⁴(95-digit number)
87747285350694782457…09895832791794050001
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
8.774 Γ— 10⁹⁴(95-digit number)
87747285350694782457…09895832791794050001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.754 Γ— 10⁹⁡(96-digit number)
17549457070138956491…19791665583588100001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.509 Γ— 10⁹⁡(96-digit number)
35098914140277912983…39583331167176200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.019 Γ— 10⁹⁡(96-digit number)
70197828280555825966…79166662334352400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.403 Γ— 10⁹⁢(97-digit number)
14039565656111165193…58333324668704800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.807 Γ— 10⁹⁢(97-digit number)
28079131312222330386…16666649337409600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.615 Γ— 10⁹⁢(97-digit number)
56158262624444660773…33333298674819200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.123 Γ— 10⁹⁷(98-digit number)
11231652524888932154…66666597349638400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.246 Γ— 10⁹⁷(98-digit number)
22463305049777864309…33333194699276800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.492 Γ— 10⁹⁷(98-digit number)
44926610099555728618…66666389398553600001
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:57,936,833 XPMΒ·at block #6,836,570 Β· updates every 60s
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