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Block #852,013

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2014, 6:20:37 PM Β· Difficulty 10.9702 Β· 5,974,976 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7f9c6d3e89927ae3aa430cf477a2c3ab28212a22b8689eb49aba36b8090ed025
View on Chainz β†—

Height

#852,013

Difficulty

10.970161

Transactions

2

Size

574 B

Version

2

Bits

0af85c7f

Nonce

346,551,907

Timestamp

12/13/2014, 6:20:37 PM

Confirmations

5,974,976

Mined by

⛏️ P2SHAbdE6yugxPs4Ngoba33qjZqHHGpdKFk6aw

Merkle Root

c6a7ae08d8756c704389af346179baee943867469cab2878ef1ba3305aac730f
Transactions (2)
Coinbased17ca27a6c7afb…94c0b9dac729e7
1 in β†’ 1 out8.3100 XPM110 B
AbdE6yug…pdKFk6aw
590cb9dc5e69f2…d3f6f9f7def73b
2 in β†’ 2 out14.4982 XPM374 B
AT6hERnY…5615mjajAUY54LT9…Q8pWMHVG
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.

7.152 Γ— 10⁹⁴(95-digit number)
71527224518555881932…37993210026888668959
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
7.152 Γ— 10⁹⁴(95-digit number)
71527224518555881932…37993210026888668959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.152 Γ— 10⁹⁴(95-digit number)
71527224518555881932…37993210026888668961
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
1.430 Γ— 10⁹⁡(96-digit number)
14305444903711176386…75986420053777337919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.430 Γ— 10⁹⁡(96-digit number)
14305444903711176386…75986420053777337921
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
2.861 Γ— 10⁹⁡(96-digit number)
28610889807422352772…51972840107554675839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.861 Γ— 10⁹⁡(96-digit number)
28610889807422352772…51972840107554675841
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
5.722 Γ— 10⁹⁡(96-digit number)
57221779614844705545…03945680215109351679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.722 Γ— 10⁹⁡(96-digit number)
57221779614844705545…03945680215109351681
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
1.144 Γ— 10⁹⁢(97-digit number)
11444355922968941109…07891360430218703359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.144 Γ— 10⁹⁢(97-digit number)
11444355922968941109…07891360430218703361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,860,086 XPMΒ·at block #6,826,988 Β· updates every 60s
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