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Block #584,267

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/11/2014, 8:03:56 AM Β· Difficulty 10.9552 Β· 6,211,635 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
7b8744debe4e1d52ef3dfba55e0cf076f692504459cd0310e789e884e0a4f758
View on Chainz β†—

Height

#584,267

Difficulty

10.955166

Transactions

1

Size

243 B

Version

2

Bits

0af485bf

Nonce

2,057,652,924

Timestamp

6/11/2014, 8:03:56 AM

Confirmations

6,211,635

Mined by

⛏️ P2SHAXn1KW6PTFKBcGVcbZ8CPoUc4Pc7VDu2zv

Merkle Root

ec1847ded9975498ea1682fef7895e2222ae7c3ffc498b0f4efaffead31ddd03
Transactions (1)
Coinbaseec1847ded99754…faffead31ddd03
1 in β†’ 2 out8.3200 XPM152 B
AXn1KW6P…c7VDu2zvALPu3s2c…EJXLjVFh
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.

1.569 Γ— 10⁹⁸(99-digit number)
15691396592820774000…21420414866913395199
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.569 Γ— 10⁹⁸(99-digit number)
15691396592820774000…21420414866913395199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.569 Γ— 10⁹⁸(99-digit number)
15691396592820774000…21420414866913395201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.138 Γ— 10⁹⁸(99-digit number)
31382793185641548000…42840829733826790399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.138 Γ— 10⁹⁸(99-digit number)
31382793185641548000…42840829733826790401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
6.276 Γ— 10⁹⁸(99-digit number)
62765586371283096000…85681659467653580799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.276 Γ— 10⁹⁸(99-digit number)
62765586371283096000…85681659467653580801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.255 Γ— 10⁹⁹(100-digit number)
12553117274256619200…71363318935307161599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.255 Γ— 10⁹⁹(100-digit number)
12553117274256619200…71363318935307161601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.510 Γ— 10⁹⁹(100-digit number)
25106234548513238400…42726637870614323199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.510 Γ— 10⁹⁹(100-digit number)
25106234548513238400…42726637870614323201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
5.021 Γ— 10⁹⁹(100-digit number)
50212469097026476800…85453275741228646399
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,611,300 XPMΒ·at block #6,795,901 Β· updates every 60s
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