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Block #163,821

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/14/2013, 6:27:27 AM Β· Difficulty 9.8618 Β· 6,644,412 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
30faf81bc4e2cea5db46540e01d00f67e8904c0a9cee7d75b38061d946066d40
View on Chainz β†—

Height

#163,821

Difficulty

9.861814

Transactions

1

Size

197 B

Version

2

Bits

09dc9fda

Nonce

204,094

Timestamp

9/14/2013, 6:27:27 AM

Confirmations

6,644,412

Mined by

⛏️ P2SHAX99MLNmm1FbkFRt6WY4Zu9rUBvtidqEwE

Merkle Root

fe01616bcc5b2b585b74abf52221b9413f524c16008c044d779add8d82ce6bba
Transactions (1)
Coinbasefe01616bcc5b2b…9add8d82ce6bba
1 in β†’ 1 out10.2700 XPM109 B
AX99MLNm…vtidqEwE
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.

9.625 Γ— 10⁹⁰(91-digit number)
96255462699949438246…06449964228411623839
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
9.625 Γ— 10⁹⁰(91-digit number)
96255462699949438246…06449964228411623839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.625 Γ— 10⁹⁰(91-digit number)
96255462699949438246…06449964228411623841
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
1.925 Γ— 10⁹¹(92-digit number)
19251092539989887649…12899928456823247679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.925 Γ— 10⁹¹(92-digit number)
19251092539989887649…12899928456823247681
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
3.850 Γ— 10⁹¹(92-digit number)
38502185079979775298…25799856913646495359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.850 Γ— 10⁹¹(92-digit number)
38502185079979775298…25799856913646495361
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
7.700 Γ— 10⁹¹(92-digit number)
77004370159959550597…51599713827292990719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.700 Γ— 10⁹¹(92-digit number)
77004370159959550597…51599713827292990721
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
1.540 Γ— 10⁹²(93-digit number)
15400874031991910119…03199427654585981439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.540 Γ— 10⁹²(93-digit number)
15400874031991910119…03199427654585981441
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:57,709,917 XPMΒ·at block #6,808,232 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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