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Block #902,586

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/20/2015, 11:37:05 AM Β· Difficulty 10.9397 Β· 5,913,503 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2f62cda39602bd1f64f8eb4e8a55c70277b582775242084be49f96622077fd87
View on Chainz β†—

Height

#902,586

Difficulty

10.939694

Transactions

2

Size

1.14 KB

Version

2

Bits

0af08fc7

Nonce

942,620,444

Timestamp

1/20/2015, 11:37:05 AM

Confirmations

5,913,503

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

21c51bda0f5860c7821e0bfee841a9a02dc5b89ae85fec8fbca3cb937845d67d
Transactions (2)
Coinbase1a7c555fcbca40…95c5a0fbbc29d8
1 in β†’ 1 out8.3500 XPM116 B
ANSXnLY2…Sd25TjkD
2135f2c0136f6b…75fae108d64bf0
6 in β†’ 2 out887.0212 XPM967 B
AUSxVrre…B27XD3yvAYpd51U8…xSyzg4J5
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.

2.383 Γ— 10⁹³(94-digit number)
23838183357520594299…70038367349131246671
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
2.383 Γ— 10⁹³(94-digit number)
23838183357520594299…70038367349131246671
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.767 Γ— 10⁹³(94-digit number)
47676366715041188599…40076734698262493341
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.535 Γ— 10⁹³(94-digit number)
95352733430082377199…80153469396524986681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.907 Γ— 10⁹⁴(95-digit number)
19070546686016475439…60306938793049973361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.814 Γ— 10⁹⁴(95-digit number)
38141093372032950879…20613877586099946721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.628 Γ— 10⁹⁴(95-digit number)
76282186744065901759…41227755172199893441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.525 Γ— 10⁹⁡(96-digit number)
15256437348813180351…82455510344399786881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.051 Γ— 10⁹⁡(96-digit number)
30512874697626360703…64911020688799573761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.102 Γ— 10⁹⁡(96-digit number)
61025749395252721407…29822041377599147521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.220 Γ— 10⁹⁢(97-digit number)
12205149879050544281…59644082755198295041
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:57,772,831 XPMΒ·at block #6,816,088 Β· updates every 60s
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