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Block #2,169,056

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/20/2017, 4:40:10 PM Β· Difficulty 10.8987 Β· 4,668,327 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
583d15ffa6d57a422557c83eeecfae1c24b1e3b6b365366f6a894ffa277df538
View on Chainz β†—

Height

#2,169,056

Difficulty

10.898744

Transactions

2

Size

721 B

Version

2

Bits

0ae61416

Nonce

700,789,356

Timestamp

6/20/2017, 4:40:10 PM

Confirmations

4,668,327

Mined by

⛏️ P2SHAeSw9RquYXxSqmPGzBCofHdkQ8Euo28jbx

Merkle Root

d6c61e0fbefd24a658ef6d0da1d12af5fed1639a4a655fe2afff9aed37838651
Transactions (2)
Coinbase4ac26d6bdb3967…0fa8b06096f195
1 in β†’ 1 out8.5100 XPM109 B
AeSw9Rqu…Euo28jbx
93582e9613dc73…777529ad0c0443
3 in β†’ 2 out561.8508 XPM523 B
Aebn325e…kXZo48uYAZuAB317…a9CbPqhC
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.

7.062 Γ— 10⁹¹(92-digit number)
70628820000378377165…67700333383927280809
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
7.062 Γ— 10⁹¹(92-digit number)
70628820000378377165…67700333383927280809
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.062 Γ— 10⁹¹(92-digit number)
70628820000378377165…67700333383927280811
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
1.412 Γ— 10⁹²(93-digit number)
14125764000075675433…35400666767854561619
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.412 Γ— 10⁹²(93-digit number)
14125764000075675433…35400666767854561621
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
2.825 Γ— 10⁹²(93-digit number)
28251528000151350866…70801333535709123239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.825 Γ— 10⁹²(93-digit number)
28251528000151350866…70801333535709123241
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
5.650 Γ— 10⁹²(93-digit number)
56503056000302701732…41602667071418246479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.650 Γ— 10⁹²(93-digit number)
56503056000302701732…41602667071418246481
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
1.130 Γ— 10⁹³(94-digit number)
11300611200060540346…83205334142836492959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.130 Γ— 10⁹³(94-digit number)
11300611200060540346…83205334142836492961
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
2.260 Γ— 10⁹³(94-digit number)
22601222400121080693…66410668285672985919
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:57,943,386 XPMΒ·at block #6,837,382 Β· updates every 60s
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