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Block #622,020

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/7/2014, 6:32:43 PM Β· Difficulty 10.9532 Β· 6,177,556 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5aaf9f28d7476cb5a47afed6db4191124822698346155a106ef47184d60dcbba
View on Chainz β†—

Height

#622,020

Difficulty

10.953247

Transactions

1

Size

697 B

Version

2

Bits

0af407fb

Nonce

88,246

Timestamp

7/7/2014, 6:32:43 PM

Confirmations

6,177,556

Mined by

AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

42d9be0257dfa60f600bec673b032ded91890cc2f39e9587f0231379b620d594
Transactions (1)
Coinbase42d9be0257dfa6…231379b620d594
1 in β†’ 16 out8.3200 XPM607 B
AQvZBsUo…hppgRZTJAJzWx2VD…j4ZSMit5AQyr8Lw3…hs4nt3PnAJ19VDo9…9iY1XZACAcVAEuoP…1jK61Unr
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.

3.215 Γ— 10⁹⁴(95-digit number)
32150186146927550562…98483877587231886399
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
3.215 Γ— 10⁹⁴(95-digit number)
32150186146927550562…98483877587231886399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.215 Γ— 10⁹⁴(95-digit number)
32150186146927550562…98483877587231886401
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
6.430 Γ— 10⁹⁴(95-digit number)
64300372293855101124…96967755174463772799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.430 Γ— 10⁹⁴(95-digit number)
64300372293855101124…96967755174463772801
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
1.286 Γ— 10⁹⁡(96-digit number)
12860074458771020224…93935510348927545599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.286 Γ— 10⁹⁡(96-digit number)
12860074458771020224…93935510348927545601
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
2.572 Γ— 10⁹⁡(96-digit number)
25720148917542040449…87871020697855091199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.572 Γ— 10⁹⁡(96-digit number)
25720148917542040449…87871020697855091201
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
5.144 Γ— 10⁹⁡(96-digit number)
51440297835084080899…75742041395710182399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.144 Γ— 10⁹⁡(96-digit number)
51440297835084080899…75742041395710182401
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
1.028 Γ— 10⁹⁢(97-digit number)
10288059567016816179…51484082791420364799
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:57,640,657 XPMΒ·at block #6,799,575 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK