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Block #377,765

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/27/2014, 8:56:58 AM Β· Difficulty 10.4189 Β· 6,420,804 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
01604082fac55d5bac29b5d7d04ec944c70f8b012ebfc2f4663d5371b7f50e4f
View on Chainz β†—

Height

#377,765

Difficulty

10.418892

Transactions

2

Size

394 B

Version

2

Bits

0a6b3c82

Nonce

241,189

Timestamp

1/27/2014, 8:56:58 AM

Confirmations

6,420,804

Mined by

⛏️ P2SHAM5ppYffQNAgWqt4meKF85MHAWgx4KUH3E

Merkle Root

a65c50415d7451f07da03dbea11e3feb2cdd8742a37fa7eeb5d2b1a804434e3b
Transactions (2)
Coinbaseaa718155edbb0b…87be18570b4d54
1 in β†’ 1 out9.2100 XPM111 B
AM5ppYff…gx4KUH3E
d6202f5b1a1983…f0aa65d4a36368
1 in β†’ 1 out16.9900 XPM192 B
AWEEVTE7…HHVYFX5v
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.

2.581 Γ— 10⁹⁷(98-digit number)
25814553345202667849…60274797691828288001
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
2.581 Γ— 10⁹⁷(98-digit number)
25814553345202667849…60274797691828288001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.162 Γ— 10⁹⁷(98-digit number)
51629106690405335699…20549595383656576001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.032 Γ— 10⁹⁸(99-digit number)
10325821338081067139…41099190767313152001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.065 Γ— 10⁹⁸(99-digit number)
20651642676162134279…82198381534626304001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.130 Γ— 10⁹⁸(99-digit number)
41303285352324268559…64396763069252608001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.260 Γ— 10⁹⁸(99-digit number)
82606570704648537119…28793526138505216001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.652 Γ— 10⁹⁹(100-digit number)
16521314140929707423…57587052277010432001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.304 Γ— 10⁹⁹(100-digit number)
33042628281859414847…15174104554020864001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.608 Γ— 10⁹⁹(100-digit number)
66085256563718829695…30348209108041728001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.321 Γ— 10¹⁰⁰(101-digit number)
13217051312743765939…60696418216083456001
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:57,632,570 XPMΒ·at block #6,798,568 Β· updates every 60s
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