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Block #849,051

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/11/2014, 1:25:37 PM Β· Difficulty 10.9713 Β· 5,991,492 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
005e148e4e88d6d7a6a31e1e7bfb73e76af384bc0da160b61993e690585e18c5
View on Chainz β†—

Height

#849,051

Difficulty

10.971299

Transactions

2

Size

433 B

Version

2

Bits

0af8a711

Nonce

848,894,456

Timestamp

12/11/2014, 1:25:37 PM

Confirmations

5,991,492

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4262f71115e13c47fe13f1b4f96716ab7c3acd8eb4db3f17c20343ac0b265255
Transactions (2)
Coinbase254f24c7fd20d4…281a68b503e782
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
9fbb3b3f2558a5…3cb8f7b9d59182
1 in β†’ 2 out0.0892 XPM226 B
AZxJXAr2…vPnhdNCJAHWPa9vt…xUQtVAaX
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.

4.310 Γ— 10⁹⁷(98-digit number)
43109475244160798961…53287167405616972801
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
4.310 Γ— 10⁹⁷(98-digit number)
43109475244160798961…53287167405616972801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.621 Γ— 10⁹⁷(98-digit number)
86218950488321597922…06574334811233945601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.724 Γ— 10⁹⁸(99-digit number)
17243790097664319584…13148669622467891201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.448 Γ— 10⁹⁸(99-digit number)
34487580195328639169…26297339244935782401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.897 Γ— 10⁹⁸(99-digit number)
68975160390657278338…52594678489871564801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.379 Γ— 10⁹⁹(100-digit number)
13795032078131455667…05189356979743129601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.759 Γ— 10⁹⁹(100-digit number)
27590064156262911335…10378713959486259201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.518 Γ— 10⁹⁹(100-digit number)
55180128312525822670…20757427918972518401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.103 Γ— 10¹⁰⁰(101-digit number)
11036025662505164534…41514855837945036801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.207 Γ— 10¹⁰⁰(101-digit number)
22072051325010329068…83029711675890073601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.414 Γ— 10¹⁰⁰(101-digit number)
44144102650020658136…66059423351780147201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,968,676 XPMΒ·at block #6,840,542 Β· updates every 60s
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