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Block #843,084

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/7/2014, 3:26:09 AM Β· Difficulty 10.9733 Β· 5,983,998 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f3b6e935823de8b3b4c3a9b816f0124d2b231f945239deb01460059906a27cb9
View on Chainz β†—

Height

#843,084

Difficulty

10.973271

Transactions

2

Size

425 B

Version

2

Bits

0af92852

Nonce

1,734,319,891

Timestamp

12/7/2014, 3:26:09 AM

Confirmations

5,983,998

Mined by

⛏️ P2SHAXh9LzCrcxAoLBLMoHywGEQjz5mDWxKeqm

Merkle Root

5244e6b9052a4d34aa51436d8871823653911018517d54630573f25e42fb5e92
Transactions (2)
Coinbaseee67d3eed95108…2f1c1891d9056a
1 in β†’ 1 out8.3050 XPM109 B
AXh9LzCr…mDWxKeqm
e6cdf53e1d4e4e…06183150b133f6
1 in β†’ 2 out0.0716 XPM226 B
AZ1BqR9m…bV35tLfiARhnmSrM…rb87yoRu
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.

4.847 Γ— 10⁹⁴(95-digit number)
48472128196750108142…08749061533747235679
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
4.847 Γ— 10⁹⁴(95-digit number)
48472128196750108142…08749061533747235679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.847 Γ— 10⁹⁴(95-digit number)
48472128196750108142…08749061533747235681
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
9.694 Γ— 10⁹⁴(95-digit number)
96944256393500216285…17498123067494471359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.694 Γ— 10⁹⁴(95-digit number)
96944256393500216285…17498123067494471361
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
1.938 Γ— 10⁹⁡(96-digit number)
19388851278700043257…34996246134988942719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.938 Γ— 10⁹⁡(96-digit number)
19388851278700043257…34996246134988942721
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
3.877 Γ— 10⁹⁡(96-digit number)
38777702557400086514…69992492269977885439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.877 Γ— 10⁹⁡(96-digit number)
38777702557400086514…69992492269977885441
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
7.755 Γ— 10⁹⁡(96-digit number)
77555405114800173028…39984984539955770879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.755 Γ— 10⁹⁡(96-digit number)
77555405114800173028…39984984539955770881
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
1.551 Γ— 10⁹⁢(97-digit number)
15511081022960034605…79969969079911541759
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:57,860,841 XPMΒ·at block #6,827,081 Β· updates every 60s
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