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Block #2,063,322

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/9/2017, 11:21:07 AM Β· Difficulty 10.8527 Β· 4,762,175 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e020bc3820226aa2eeae5723148839a1694bd2e7394505e4db30423575df405e
View on Chainz β†—

Height

#2,063,322

Difficulty

10.852737

Transactions

1

Size

200 B

Version

2

Bits

0ada4cfb

Nonce

565,581,779

Timestamp

4/9/2017, 11:21:07 AM

Confirmations

4,762,175

Mined by

⛏️ P2SHAN3RoqLhSY3J3i2qu6bBM5KzTJxA2vwBop

Merkle Root

4221e93aaf85b5df54e71021f8fd311db93421ee4bc729ac168d57fb20669ce9
Transactions (1)
Coinbase4221e93aaf85b5…8d57fb20669ce9
1 in β†’ 1 out8.4800 XPM110 B
AN3RoqLh…xA2vwBop
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.

4.619 Γ— 10⁹⁴(95-digit number)
46192833211329306063…22542671377901853079
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
4.619 Γ— 10⁹⁴(95-digit number)
46192833211329306063…22542671377901853079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.619 Γ— 10⁹⁴(95-digit number)
46192833211329306063…22542671377901853081
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
9.238 Γ— 10⁹⁴(95-digit number)
92385666422658612126…45085342755803706159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.238 Γ— 10⁹⁴(95-digit number)
92385666422658612126…45085342755803706161
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
1.847 Γ— 10⁹⁡(96-digit number)
18477133284531722425…90170685511607412319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.847 Γ— 10⁹⁡(96-digit number)
18477133284531722425…90170685511607412321
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
3.695 Γ— 10⁹⁡(96-digit number)
36954266569063444850…80341371023214824639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.695 Γ— 10⁹⁡(96-digit number)
36954266569063444850…80341371023214824641
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
7.390 Γ— 10⁹⁡(96-digit number)
73908533138126889700…60682742046429649279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.390 Γ— 10⁹⁡(96-digit number)
73908533138126889700…60682742046429649281
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
1.478 Γ— 10⁹⁢(97-digit number)
14781706627625377940…21365484092859298559
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
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