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Block #1,335,611

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/21/2015, 9:33:00 AM Β· Difficulty 10.8210 Β· 5,478,705 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0a2b4e1309b64d491e42ae969f2d38dc44ab0ed46401b688cccbfbe9d81f9e23
View on Chainz β†—

Height

#1,335,611

Difficulty

10.821020

Transactions

2

Size

720 B

Version

2

Bits

0ad22e58

Nonce

659,372,283

Timestamp

11/21/2015, 9:33:00 AM

Confirmations

5,478,705

Mined by

⛏️ P2SHAcHZAo99W1ku1BEbdWcbUW5WqwtG3NMRzR

Merkle Root

e3eaef2838dc2cd1c97b28bebe109c35fe336fa678c7c5ccdc319a950b14c1e5
Transactions (2)
Coinbase995b6adcc26a9d…833c1fe6710383
1 in β†’ 1 out8.5400 XPM109 B
AcHZAo99…tG3NMRzR
107f28835318ca…9f270329034355
3 in β†’ 2 out2.2100 XPM521 B
AFwbeT2h…ZY4neVQTAesJVMS3…WrAkHdm5
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.

3.839 Γ— 10⁹⁴(95-digit number)
38399827403764875895…16173669165951701439
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
3.839 Γ— 10⁹⁴(95-digit number)
38399827403764875895…16173669165951701439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.839 Γ— 10⁹⁴(95-digit number)
38399827403764875895…16173669165951701441
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
7.679 Γ— 10⁹⁴(95-digit number)
76799654807529751791…32347338331903402879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.679 Γ— 10⁹⁴(95-digit number)
76799654807529751791…32347338331903402881
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
1.535 Γ— 10⁹⁡(96-digit number)
15359930961505950358…64694676663806805759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.535 Γ— 10⁹⁡(96-digit number)
15359930961505950358…64694676663806805761
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
3.071 Γ— 10⁹⁡(96-digit number)
30719861923011900716…29389353327613611519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.071 Γ— 10⁹⁡(96-digit number)
30719861923011900716…29389353327613611521
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
6.143 Γ— 10⁹⁡(96-digit number)
61439723846023801433…58778706655227223039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.143 Γ— 10⁹⁡(96-digit number)
61439723846023801433…58778706655227223041
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
1.228 Γ— 10⁹⁢(97-digit number)
12287944769204760286…17557413310454446079
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:57,758,591 XPMΒ·at block #6,814,315 Β· updates every 60s
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