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Block #2,783,182

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2018, 10:46:51 AM Β· Difficulty 11.6609 Β· 4,059,991 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3b96466f73b576592e77f7e028473249225271c5142ac669e3b72bbe9c9ab2da
View on Chainz β†—

Height

#2,783,182

Difficulty

11.660865

Transactions

1

Size

201 B

Version

2

Bits

0ba92e74

Nonce

204,923,298

Timestamp

8/7/2018, 10:46:51 AM

Confirmations

4,059,991

Mined by

⛏️ P2SHASANgYxKU59j16ZC19UfdMo6AejH9bsN39

Merkle Root

67e368329be550b2131f28812705b7b91346ce16dc9f8a443eb4cf104dd8316e
Transactions (1)
Coinbase67e368329be550…b4cf104dd8316e
1 in β†’ 1 out7.3400 XPM110 B
ASANgYxK…jH9bsN39
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.

1.614 Γ— 10⁹⁸(99-digit number)
16143249509336990114…26506451813317017599
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
1.614 Γ— 10⁹⁸(99-digit number)
16143249509336990114…26506451813317017599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.614 Γ— 10⁹⁸(99-digit number)
16143249509336990114…26506451813317017601
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
3.228 Γ— 10⁹⁸(99-digit number)
32286499018673980228…53012903626634035199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.228 Γ— 10⁹⁸(99-digit number)
32286499018673980228…53012903626634035201
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
6.457 Γ— 10⁹⁸(99-digit number)
64572998037347960457…06025807253268070399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.457 Γ— 10⁹⁸(99-digit number)
64572998037347960457…06025807253268070401
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
1.291 Γ— 10⁹⁹(100-digit number)
12914599607469592091…12051614506536140799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.291 Γ— 10⁹⁹(100-digit number)
12914599607469592091…12051614506536140801
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
2.582 Γ— 10⁹⁹(100-digit number)
25829199214939184183…24103229013072281599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.582 Γ— 10⁹⁹(100-digit number)
25829199214939184183…24103229013072281601
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
5.165 Γ— 10⁹⁹(100-digit number)
51658398429878368366…48206458026144563199
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:57,989,750 XPMΒ·at block #6,843,172 Β· updates every 60s
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